The Baezians were a species who were saved from extinction through the actions of James T. Kirk many years prior to the end of his five-year mission in command of the USS Enterprise.
In 2378, Icheb included this information, along with Kirk's encounters with the Pelosians and the Chenari, in his final report to Captain Kathryn Janeway, as part of the Early Starfleet History course of his Academy training. (VOY: "Q2")
This species was only mentioned in dialogue.
Details of Kirk's encounter with the Baezians are detailed in the Pocket TOS novel The Captain's Oath. Their civilization was threatened by a doomsday weapon that Kirk defused. Their homeworld was Baez IV.