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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-10-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001001614</issuerCik>
        <issuerName>Riley Exploration Permian, Inc.</issuerName>
        <issuerTradingSymbol>REPX</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001755918</rptOwnerCik>
            <rptOwnerName>Riley Philip A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>C/O RILEY EXPLORATION PERMIAN, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>29 EAST RENO, SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>OKLAHOMA CITY</rptOwnerCity>
            <rptOwnerState>OK</rptOwnerState>
            <rptOwnerZipCode>73104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CFO &amp; EVP STRATEGY</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2026-10-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6954</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>40.01</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>228549</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of common stock surrendered to the issuer to satisfy tax withholding obligations incurred upon the vesting of restricted stock granted to the reporting person under the Amended and Restated Riley Exploration Permian, Inc. 2021 Long Term Incentive Plan. The surrender is exempt under Rule 16b-3(e) and does not represent a discretionary trade by the reporting person.</footnote>
        <footnote id="F2">This amount includes 133,579 shares of restricted common stock subject to vesting and certain other restrictions.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Philip Riley</signatureName>
        <signatureDate>2026-10-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
