As a Notary, you're an identity manager. If you sense something suspicious when examining a client's identity document, ask them about the particulars on their ID such as birth date or address. You also can ask to see a secondary ID.
If the client produces a second photo ID, compare the pictures. If the background or clothing are the same, you may have been presented with fraudulent IDs. It's doubtful your signer would be wearing the exact same clothes and be in the exact same background for multiple, legitimate IDs, such as a driver's license or U.S. Passport.
In any case, use your common-sense judgment. If you remain suspicious, refuse to perform the notarization and note why you did so in your journal.