The nerve that is related to pyriform recess in pharynx:
PYRIFORM FOSSA:
It is a deep recess broad above and narrow below in the anterior part of lateral wall of the laryngopharynx, on each side of the laryngeal inlet. 
These recesses are produced due to bulging of larynx into laryngopharynx.
Boundaries:
Medial: Aryepiglottic fold and quadrangular membrane of larynx.
Lateral: Mucous membrane covering the medial surface of the lamina of thyroid cartilage and thyrohyoid membrane.
The internal laryngeal nerve and superior laryngeal vessels pierce the thyrohyoid membrane and traverse underneath the mucous membrane of the floor of the fossa to reach the medial wall.
Above: Piriform fossa is separated from epiglottic vallecula by lateral glossoepiglottic fold.
Key Concept:
Internal laryngeal nerve is the nerve related to pyriform fossa.
Recurrent laryngeal
External laryngeal
Internal laryngeal
Glosso pharyngeal