A fingerprint was a pattern on one's digits that could be used to confirm one's identity via biometrics. A fingerprint of a thumb was called a thumbprint. They were included on identity tapes. On Ferenginar, Ferengi used dermal prints as means of signatures. A thumbscan was a biometric identification consisting of an image of an individual's thumbprint.
A Cardassian's thumbprint on a Kressari PADD was all the evidence Kira Nerys needed in 2370 to prove to the Chamber of Ministers a connection between Cardassia and The Circle. Once the thumbprint established the shocking truth behind The Circle, Minister Jaro Essa's attempted a coup d'etat against the Bajoran Provisional Government immediately collapsed. (DS9: "The Siege")
Thumbprints could be used in lieu of signatures. In 2374, Luther Sloan threatened Julian Bashir with confinement in a maximum security cell for the duration of the Dominion War unless he put his thumbprint on a confession. (DS9: "Inquisition")