**Core Concept**
The question tests the clinical correlation between a valgus deformity in the elbow and paresthesias over the medial border of the hand, which is a classic presentation of a nerve injury. This is related to the anatomy and function of the ulnar nerve.

**Why the Correct Answer is Right**
The patient's symptoms suggest an injury to the ulnar nerve, which is a common complication of supracondylar fractures of the humerus. The ulnar nerve runs through a narrow osteofibrous groove in the medial epicondyle of the humerus. A valgus deformity of the elbow can cause chronic stretching and compression of the ulnar nerve, leading to paresthesias in the distribution of the ulnar nerve, which includes the medial border of the hand. This is a classic example of a "stretch injury" to the ulnar nerve.

**Why Each Wrong Option is Incorrect**
**Option A:**
This option is incorrect because it does not explain the valgus deformity or the specific distribution of paresthesias. A radial nerve injury would more likely cause paresthesias in the back of the hand.

**Option B:**
This option is incorrect because it does not account for the valgus deformity or the specific nerve involved. A median nerve injury would more likely cause paresthesias in the palmar surface of the hand.

**Option C:**
This option is incorrect because it does not explain the valgus deformity or the specific nerve involved. A common peroneal nerve injury would more likely cause foot drop.

**Clinical Pearl / High-Yield Fact**
A valgus deformity of the elbow is a classic risk factor for ulnar nerve injury, which can cause chronic stretching and compression of the nerve, leading to paresthesias in the medial border of the hand.

**Correct Answer: C. supracondylar fracture**