The Starfleet 4th Fleet was a military unit, a fleet group of the Federation Starfleet during the 2360s. In the late 24th century, the 4th fleet was a mobile fleet tasked with protecting the core planets of the Federation. (Last Unicorn RPG module: The Price of Freedom)
Elements of the 4th fleet made up the forces massed at Wolf 359 to battle the Borg in 2367. Along with the 5th and 7th Fleets, the 4th was severely decimated by that confrontation. (Decipher RPG module: Starfleet Operations Manual)