**Core Concept:**
The anterior division of the mandibular nerve (CN V3) is a branch of the trigeminal nerve, which is responsible for sensory innervation of various structures in the head and neck region. The mandibular nerve has three branches: the mental nerve, the inferior alveolar nerve, and the posterior branch.

**Why the Correct Answer is Right:**
The correct answer is C: **The inferior alveolar nerve (IAN)** is the sensory branch of the anterior division of the mandibular nerve. The IAN supplies sensory innervation to the lower teeth, buccal mucosa, and the angle of the mandible.

**Why Each Wrong Option is Incorrect:**
A: **The mental nerve** is a sensory and motor branch of the mandibular nerve, responsible for innervating the mental region of the chin and the skin of the chin, but not the teeth or buccal mucosa.
B: **The posterior branch** of the mandibular nerve supplies motor innervation to the muscles of mastication but not sensory innervation.
D: **The posterior auricular nerve** is a branch of the posterior division of the mandibular nerve, supplying sensory innervation to the posterior aspect of the ear, not related to the teeth or buccal mucosa.

**Clinical Pearl / High-Yield Fact:**
The inferior alveolar nerve is essential to understand during dental and oral surgery, as its section can lead to significant morbidity such as anesthesia of lower lip, chin, and teeth, and damage to the mental neurovascular bundle, which contains the inferior alveolar artery, vein, and nerve.

Please note that this explanation is tailored for NEET PG, USMLE, AIIMS, and FMGE students and is aimed to be informative and concise, while maintaining clarity on the subject matter. If you require a more detailed explanation, please let me know, and I will be happy to provide it.