C-111 system was the official designation for a planetary system. This system consisted of a primary and at least three planets. The third planet, Beta III, was the homeworld of a pre-warp capable species, the Beta III natives. (TOS: "The Return of the Archons", ENT: "In a Mirror, Darkly, Part II")
The Archon was the first vessel to explore the system in the 2160s; the ship was destroyed by the Landru entity on the third planet. In 2267, the USS Enterprise conducted a followup mission, investigating the loss of the Archon. (TOS: "The Return of the Archons")
In 2370, the USS G'Mat traveled from the C-111 system to Deep Space 9. (DS9: "Whispers")
There were other planets that were named Beta (number): Beta V, Beta VI, and Beta XII-A. It was never stated in canon what systems these planets were located in, so one or more of them might have been in this system.