It is a branch of the mandibular nerve (CN V3).

[2][better source needed] It penetrates the deep surface of the medial pterygoid muscle.

It issues 1-2 twigs which traverse the otic ganglion (without synapsing) to reach and innervate the tensor tympani muscle, and tensor veli palatini muscle.

[1] The medial pterygoid nerve supplies the medial pterygoid muscle, tensor tympani muscle, and tensor veli palatini muscle (via the nerve to tensor veli palatini).

[1] The tensor veli palati muscle is the only of the five paired skeletal muscles to the soft palate not innervated by the pharyngeal plexus.