Which muscle does not belong to the innervational territory of the median nerve?

The adductor pollicis muscle is primarily innervated by the ulnar nerve, making it the correct choice for the question regarding which muscle does not belong to the median nerve's innervational territory. The adductor pollicis has a function that is distinct from the muscles innervated by the median nerve, which generally supply muscles involved in flexion and opposition of the thumb.

In contrast, the abductor pollicis brevis (APB), opponens pollicis (OP), and first dorsal interosseous (FDI) are all innervated by the median nerve. The APB and OP are responsible for movements of abduction and opposition of the thumb, while the FDI is involved in abducting the index finger and assisting in various hand functions. Thus, these muscles are all directly connected to the median nerve's functional domain, further contrasting with the adductor pollicis.