The middle superior alveolar nerve is a nerve

Nerve

A peripheral nerve, or simply nerve, is an enclosed, cable-like bundle of peripheral axons . A nerve provides a common pathway for the electrochemical nerve impulses that are transmitted along each of the axons. Nerves are found only in the peripheral nervous system...

 that drops from the infraorbital portion of the maxillary nerve to supply the sinus mucosa, the roots of the maxillary premolars, and the mesiobuccal root of the first maxillary molar.
It is not always present; and in the majority of cases it is non existent with the posterior superior alveolar nerve

Posterior superior alveolar nerve

The posterior superior alveolar branches arise from the trunk of the maxillary nerve just before it enters the infraorbital groove; they are generally two in number, but sometimes arise by a single trunk....

innervating the premolars and molars alone.