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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2026-01-22</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0002083910</issuerCik>
        <issuerName>Archimedes Tech SPAC Partners III Co.</issuerName>
        <issuerTradingSymbol>ARCI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001793149</rptOwnerCik>
            <rptOwnerName>Sheehan Daniel L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2093 PHILADELPHIA PIKE #1968</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CLAYMONT</rptOwnerCity>
            <rptOwnerState>DE</rptOwnerState>
            <rptOwnerZipCode>19703</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <ownerSignature>
        <signatureName>/s/ Daniel L. Sheehan</signatureName>
        <signatureDate>2026-01-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
