In which of these letters does Paul call himself 'a prisoner of Christ Jesus' in the opening verse?

Answer: Philemon

Philemon opens, "Paul, a prisoner of Christ Jesus, and Timothy our brother"; Romans, Galatians and 1 Corinthians open with 'servant' or 'apostle'.

“Paul, a prisoner of Christ Jesus, and Timothy our brother, To Philemon our beloved fellow worker,”— Philemon 1:1 (BSB)