**Core Concept**
The question requires knowledge of the motor and sensory innervation of the hand, specifically the ulnar nerve, which is responsible for controlling the muscles of the hypothenar eminence and providing sensation to the little and ring fingers.

**Why the Correct Answer is Right**
The ulnar nerve arises from the medial cord of the brachial plexus and innervates the muscles of the hypothenar eminence (opponens digiti minimi, flexor digiti minimi, and abductor digiti minimi), as well as providing sensation to the little and ring fingers via the palmar cutaneous branch and the dorsal branch of the ulnar nerve. Atrophy of the hypothenar muscles and numbness of the little and ring fingers are classic signs of ulnar nerve damage.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the median nerve is responsible for innervating the muscles of the thenar eminence (thumb) and providing sensation to the thumb, index, and middle fingers. Damage to the median nerve would not result in atrophy of the hypothenar muscles.

**Option B:** This option is incorrect because the radial nerve is responsible for innervating the extensor muscles of the forearm and providing sensation to the back of the hand and fingers. Damage to the radial nerve would not result in atrophy of the hypothenar muscles or numbness of the little and ring fingers.

**Option C:** This option is incorrect because the musculocutaneous nerve is responsible for innervating the biceps brachii and brachialis muscles, and providing sensation to the lateral aspect of the forearm. Damage to the musculocutaneous nerve would not result in atrophy of the hypothenar muscles or numbness of the little and ring fingers.

**Option D:** This option is incorrect because the axillary nerve is responsible for innervating the deltoid and teres minor muscles, and providing sensation to the lateral aspect of the shoulder. Damage to the axillary nerve would not result in atrophy of the hypothenar muscles or numbness of the little and ring fingers.

**Clinical Pearl / High-Yield Fact**
The ulnar nerve is often damaged at the elbow, resulting in a condition known as "cubital tunnel syndrome." This is often caused by direct pressure on the nerve as it passes through the cubital tunnel, leading to numbness and weakness in the hand.

**Correct Answer:** C. Ulnar nerve.