Parathyroid develops from:
Parathyroid gland develops from 3rd and 4th branchial or pharyngeal pouches. Superior parathyroid develop from the 4th pharyngeal pouch and inferior parathyroid develop from the 3rd pharyngeal pouch. Ref: Langman's medical Embryology, 9th Edition, Page 384.
Branchial cyst
Branchial cleft
Branchial pouch
Branchial arch