<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-06-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001913971</issuerCik>
        <issuerName>Princeton Bancorp, Inc.</issuerName>
        <issuerTradingSymbol>BPRN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001957241</rptOwnerCik>
            <rptOwnerName>Giacin Judith A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>183 BAYARD LANE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PRINCETON</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>08540</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stocks</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-06-27</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2023-06-29</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>I</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>720</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.76</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>720</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2076</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of phantom stock is the economic equivalent of one share of BPRN common stock. The shares of phantom stock become payable, in cash or common stock, at the election of the reporting person, upon the reporting person's termination of service as a director.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Judith Giacin, by Edward Hogan as attorney-in-fact</signatureName>
        <signatureDate>2023-06-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
