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<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-07-14</periodOfReport>

    <issuer>
        <issuerCik>0001842939</issuerCik>
        <issuerName>ALPHA HEALTHCARE ACQUISITION CORP III</issuerName>
        <issuerTradingSymbol>CTCX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001984167</rptOwnerCik>
            <rptOwnerName>Godward Donna</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CARMELL THERAPEUTICS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>2403 SIDNEY STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>PITTSBURGH</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15203</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Quality Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>37296</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                    <value>37296</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
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    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.79</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>2090</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            </exerciseDate>
            <expirationDate>
                <value>2027-06-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2090</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>2090</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.27</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>5318</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-07-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5318</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5318</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
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        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.11</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>119098</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-09-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>119098</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>119098</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.11</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12309</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-07-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12309</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12309</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.60</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12309</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-12-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12309</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12309</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On July 14, 2023, Alpha Healthcare Acquisition Corp. III (&quot;ALPA&quot;) consummated a business combination (the &quot;Business Combination&quot;) by and among ALPA, Candy Merger Sub, Inc., a Delaware Corporation (&quot;Merger Sub&quot;) and Carmell Regen Med Corporation, a Delaware corporation (&quot;Legacy Carmell&quot;), ALPA changed its name to &quot;Carmell Therapeutics Corporation&quot; and Merger Sub merged with and into Legacy Carmell.  As part of the Business Combination, each share of common stock of Legacy Carmell was exchanged for 0.06154 shares of common stock of Carmell Therapeutics Corporation.</footnote>
        <footnote id="F2">Options are fully vested and exercisable.</footnote>
        <footnote id="F3">Options to purchase 5,318 shares of common stock of Legacy Carmell granted on July 19, 2019, which vest as follows: 25% vested on July 19, 2020, July 19, 2021 and July 19, 2022 and the remaining 25% becomes vested on July 19, 2023.</footnote>
        <footnote id="F4">Options to purchase 119,098 shares of common stock of Legacy Carmell granted on September 23, 2021, which vest as follows: 25% vested on September 23, 2022 and the remaining 75% becomes vested in 36 equal monthly installments thereafter, subject to continued service through each vesting date.</footnote>
        <footnote id="F5">Options to purchase 12,309 shares of common stock of Legacy Carmell granted on July 13, 2023 and the remaining 75% becomes vested in 36 equal monthly installments thereafter, subject to continued service through each vesting date.</footnote>
        <footnote id="F6">Options to purchase 12,309 shares of common stock of Legacy Carmell  granted on December 15, 2022, which vest as follows: 25% vesting on December 22, 2023 and the remaining 75% becomes vested in 36 equal monthly installments thereafter, subject to continued service through each vesting date.</footnote>
        <footnote id="F7">As part of the Business Combination, each Legacy Carmell stock option was exchanged for a stock option to acquire 0.06154 shares of common stock of Carmell Therapeutics Corporation.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Randolph W. Hubbell, Attorney-in-Fact</signatureName>
        <signatureDate>2023-07-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
