<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-23</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000924960</issuerCik><issuerName>FIRST COMMUNITY CORP /TN/</issuerName>        <issuerTradingSymbol>none</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001245138</rptOwnerCik><rptOwnerName>KRICKBAUM WILLIAM J</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>P.O. BOX 820</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>ROGERSVILLE</rptOwnerCity><rptOwnerState>TN</rptOwnerState><rptOwnerZipCode>37857</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-09-23</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1200</value></transactionShares><transactionPricePerShare><value>15.25</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>98873</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Stock Option</value></securityTitle><conversionOrExercisePrice><value>7.33</value></conversionOrExercisePrice><transactionDate><value>2003-09-23</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>120</value></transactionShares><transactionPricePerShare><value>7.33</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-09-23</value></exerciseDate><expirationDate><value>2004-04-25</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>120</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2625</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Stock Option</value></securityTitle><conversionOrExercisePrice><value>9.33</value></conversionOrExercisePrice><transactionDate><value>2003-09-23</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>90</value></transactionShares><transactionPricePerShare><value>9.33</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-09-23</value></exerciseDate><expirationDate><value>2005-04-25</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>90</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2535</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>William J. Krickbaum</signatureName><signatureDate>2003-09-24</signatureDate></ownerSignature></ownershipDocument>

