**Core Concept:**
The supracondylar fracture is a type of elbow fracture that occurs in children, typically due to a fall onto an outstretched hand. Interphalangeal joint of thumb is innervated by the ulnar nerve, which plays a crucial role in sensation and motor function of the thumb.

**Why the Correct Answer is Right:**
In the context of a supracondylar fracture, the most likely injury involves the ulnar nerve, which is responsible for the sensation and motor function of the thumb. The ulnar nerve is responsible for innervating the interphalangeal joint of the thumb, and injury to this nerve would result in inability to flex the interphalangeal joint of the thumb.

**Why Each Wrong Option is Incorrect:**
A. Radial nerve: This nerve is responsible for the motor function of the thumb and would not be primarily involved in innervating the interphalangeal joint.
B. Deep branch of radial nerve: This branch is responsible for the motor function of the thumb but not the innervation of the interphalangeal joint.
C. Ulnar nerve: This nerve is responsible for the motor function of the thumb and innervates the interphalangeal joint, making it the incorrect option.
D. Other nerves: The correct answer is related to the ulnar nerve, not any other nerves.

**Clinical Pearl:**
The ulnar nerve, also known as the "little finger nerve," is a crucial structure that helps maintain the function and sensation of the thumb. Understanding the anatomy of the ulnar nerve and its role in thumb innervation is essential for diagnosing and treating various neurological conditions involving the thumb.

**Correct Answer:** Ulnar nerve (Option C)

**Correct Answer: Ulnar nerve**

The correct answer is the ulnar nerve, as it is responsible for the motor function of the thumb and innervates the interphalangeal joint of the thumb. Injuries to the ulnar nerve can lead to a condition called "dropped thumb" or "Guyon's canal syndrome," where the thumb is unable to flex. This can be a result of compression or trauma to the ulnar nerve within Guyon's canal, a tunnel at the wrist where the ulnar nerve passes.