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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-03-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001794669</issuerCik>
        <issuerName>Shift4 Payments, Inc.</issuerName>
        <issuerTradingSymbol>FOUR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001805608</rptOwnerCik>
            <rptOwnerName>Isaacman Jared</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2202 N. IRVING ST</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ALLENTOWN</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>18109</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Forward Sale Contract (obligation to sell)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-03-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2000000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2000000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On March 16, 2021, Rook SPV 1, LLC (&quot;Rook SPV&quot;) entered into a prepaid variable forward transaction with an unaffiliated third party. The transaction obligates Rook SPV to deliver to the counterparty up to 2,000,000 shares of the Issuer's Class A Common Stock (or at Rook SPV's election, an equivalent amount of cash) on specified dates in February, March and April of 2023. In exchange for assuming this obligation, Rook SPV received a cash payment of $131,745,600. Rook SPV has pledged 2,000,000 LLC interests in Shift4 Payments, LLC (the &quot;LLC Interests&quot;) and an equal number of shares of Class B Common Stock of the Issuer (together with the LLC Interests, the &quot;Pledged Securities&quot;)</footnote>
        <footnote id="F2">(Continued from footnote 1)  to secure its obligations under the contract. Rook SPV received the Pledged Securities from Rook Holdings Inc. in a transaction exempt from reporting pursuant to Rule 16a-13. Rook SPV will retain voting and certain dividend rights in the Pledged Shares during the term of the transaction but may be required to make cash payments upon the occurrence of certain dividends declared prior to settlement.</footnote>
        <footnote id="F3">The LLC Interests generally may be redeemed by Rook SPV at any time for shares of Class A Common Stock on a 1-to-1 basis. Upon redemption of any LLC Interests, a corresponding number of shares of Class B Common Stock will be cancelled for no consideration. Prior to settlement, Rook SPV will not be permitted to exchange, transfer or otherwise dispose of the Pledged Securities (other than in connection with the settlement of the contract) and will, at all times, maintain the ability to cover its delivery obligations under the contract.</footnote>
        <footnote id="F4">The transaction is divided into 30 individual components (each comprising 66,667 shares (or 66,666 in the case of the first 10 valuation dates) (the &quot;Component Shares&quot;) of Class A Common Stock) over the 30 trading days up to, and including, April 5, 2023 (the &quot;Valuation Period&quot;). The number of Class A Common Stock to be delivered to the counterparty with respect to each component at settlement will be based on the volume weighted average price per share of the Class A Common Stock for each trading day during the Valuation Period (the &quot;Settlement Price&quot;) as follows: (A) if the Settlement Price for any component is less than or equal to $73.1920 (the &quot;Floor Price&quot;), Rook SPV will deliver for that component the Component Shares; (B) if the Settlement Price for any component is less than or equal to $137.2350 (the &quot;Cap Price&quot;), but greater than the Floor Price,</footnote>
        <footnote id="F5">(Continued from footnote 4) Rook SPV will deliver for that component a number of Class A Common Stock equal to (i) the Component Shares, multiplied by a fraction, the numerator of which is the Floor Price and the denominator of which is the Settlement Price; and (C) if the Settlement Price for any component is greater than the Cap Price, Rook SPV will deliver for that component a number of shares equal to (i) the Component Shares, multiplied by (ii) a fraction, the numerator of which is the sum of (x) the Floor Price and (y) the Settlement Price minus the Cap Price, and the denominator of which is the Settlement Price, in each case rounded up to the nearest whole share.</footnote>
        <footnote id="F6">Rook SPV is a wholly owned subsidiary of Rook Holdings Inc. Mr. Isaacman is the sole stockholder of Rook Holdings Inc. and therefore may be deemed to beneficially own the securities held of record by Rook SPV and Rook Holdings Inc.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jordan Frankel, Attorney-in-Fact for Jared Isaacman</signatureName>
        <signatureDate>2021-03-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
