Starbase 50 was a Starfleet facility in operation in the mid to late 24th century. In 2372, following the arrest of Cadet Bael Nomine for his role in the "Leyton Affair", his holographic equipment was held in impound at Starbase 50. In early 2373, that equipment was stolen by Klingon agents, who used it to lure Captains Jean-Luc Picard and Benjamin Sisko to a remote world in the Badlands. (TNG - Slings and Arrows eBook: Enterprises of Great Pitch and Moment)