Step 1: The principle is simple - a nerve block is confirmed by checking the skin area that the nerve normally supplies. Loss of pinprick or touch there means the anaesthetic has worked.
Step 2: The median nerve carries sensation from the palmar thumb, index, middle finger and the lateral half of the ring finger. So testing over the lateral aspect of the ring finger probes a median-nerve zone and reports on the adequacy of that block.
Step 3: Comparing the alternatives, the ulnar nerve covers the little finger and the medial ring finger, the radial nerve handles the dorsal hand and forearm, and the mandibular nerve is a facial sensory branch of the trigeminal. None of these is checked over the lateral ring finger, which keeps the median nerve as the structure tested.
\[\boxed{\text{Median nerve}}\]