A warden, also known as a jailer or keeper, was someone who oversaw the operation of a prison or detention facility.
In 2254, Captain Christopher Pike told Vina to tell the Talosian jailers that he wouldn't play along with their plans. He refused to be an an animal performing for its supper. (TOS: "The Cage", "The Menagerie, Part I")
In 2366, Roga Danar asked Counselor Deanna Troi if she was the keeper of the jail he was in, which was the brig of the USS Enterprise-D. When she replied that she was a counselor, he said he wished she was a jailer so she could keep him company during the trip back to Lunar V. (TNG: "The Hunted")
In 2369, Worf found it odd that his jailer Tokath asked if the Klingon wanted him to return later, remarking, "It is a strange thing when a jailer concerns himself with his prisoner's comfort." Tokath later explained that his reasons for not wishing Worf to free the Klingon captives he lived with were personal. He had come to think of them as family, and wished to protect them, not merely jail them. (TNG: "Birthright, Part II")
The Akritirian maximum security detention facility had no wardens or other personnel within it, as the facility was in space with no means for the prisoners to leave or reason to control them. (VOY: "The Chute")