Step 1: Understanding the Question.
Sarcoidosis is a disease that forms non-caseating granulomas in many organs, including the nervous system. Neurological involvement, called neurosarcoidosis, can affect the cranial nerves, and this question asks which one is affected most often.
Step 2: Key Concept.
The facial nerve (VII) is the cranial nerve most often hit in neurosarcoidosis, causing unilateral or bilateral facial weakness. It is part of Heerfordt syndrome, also called uveoparotid fever, which combines parotid gland swelling, uveitis, fever, and facial nerve palsy.
Step 3: Detailed Explanation.
Option (1) II (optic) nerve: granulomas can inflame the optic nerve and cause optic neuritis or papilloedema, but this is far less common than facial nerve involvement.
Option (2) III (oculomotor) nerve: oculomotor palsy is a recognized but uncommon feature of neurosarcoidosis.
Option (3) VII (facial) nerve: this is the cranial nerve most frequently affected, giving facial weakness that can look like Bell's palsy and is often bilateral, a pattern that should raise suspicion for sarcoidosis.
Option (4) IX (glossopharyngeal) nerve: involvement of this nerve in sarcoidosis is rare.
Step 4: Final Answer.
The facial nerve is the cranial nerve most commonly involved in sarcoidosis.
\[ \boxed{\text{VII Cranial nerve}} \]