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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-08-18</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>2026-08-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>37.6051</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>235503</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported reflects the weighted average sale price. These shares were sold in multiple transactions at prices ranging from $37.5375 to $37.6300, inclusive. These open market sale transactions were made on the same day at different prices through a trade order executed by a broker-dealer. The reporting person has reported on a single line all such transactions that occurred within a one dollar price range. The reporting person hereby undertakes to provide upon request by the Securities and Exchange Commission staff, the issuer or a security holder of the issuer, full information regarding the number of shares sold at each separate price within the range set forth in this footnote</footnote>
        <footnote id="F2">This amount includes 148,582 shares of restricted common stock subject to vesting and certain other restrictions.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Philip Riley</signatureName>
        <signatureDate>2026-08-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
