<?xml version="1.0"?>
<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>0001076972</rptOwnerCik>
            <rptOwnerName>NEWLIN WILLIAM R</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>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1249062</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Newlin Investment 1 LLC</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <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>108167</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-09-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>108167</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>108167</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.7107</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>482</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-09-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>482</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>482</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Newlin Investment 1 LLC</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.3937</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-07-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>35304</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-09-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>35304</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>35304</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Newlin Investment 1 LLC</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Newlin is Chairman and Founder of Newlin Investment 1 LLC. By virtue of this relationship, Mr. Newlin may be deemed to share beneficial ownership of the securities held of record by Newlin Investment 1 LLC. Mr. Newlin disclaims any such beneficial ownership except to the extent of his pecuniary interest.</footnote>
        <footnote id="F2">Options to purchase 108,167 shares of common stock of Legacy Carmell (as defined below) granted on September 23, 2021, which vest as follows: 25% vested on September 23, 2021 and the remaining 75% becomes vested in 36 equal monthly installments thereafter, subject to continued service through each vesting date.</footnote>
        <footnote id="F3">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 Legacy Carmell stock option was exchanged for a stock option to acquire 0.06154 shares of common stock of Carmell Therapeutics Corporation.</footnote>
        <footnote id="F4">These warrants are currently exercisable.</footnote>
        <footnote id="F5">As part of the Business Combination, (i) existing warrants to purchase common stock of Legacy Carmell were exchanged for 0.06154 warrants to purchase shares of common stock of Carmell Therapeutics Corporation and (ii) existing Series C-1 warrants to purchase common stock of Legacy Carmell were exchanged for 0.06684 warrants to purchase 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>
