(covers information from several alternate timelines)
Omicron Ceti was the primary of the Omicron Ceti star system. There was an inhabited planet, Omicron Ceti III, in this system. This planet was the location for a Federation colony in the 23rd and 24th centuries. (TOS: "This Side of Paradise"; TNG: "Eye of the Beholder")
Background information Edit
The star Omicron Ceti was depicted twice in the tactical display that marked the location of Omicron Ceti near Altair III. Based on "The Explored Galaxy" star chart and dialog from DS9: "Call to Arms", the area of space between Romulus and the Tholian Assembly was located in the Alpha Quadrant, as the two were referred to as Alpha Quadrant powers in the episode.
In the real world Omicron Ceti is also known as Mira. In the Star Trek universe however, the name Mira is used as an alternative shorter name for the red giant star Mira Antlia of the Mira system visited by the Enterprise-D in TNG: "Conspiracy". According to Star Trek: Star Charts (pg. 37), Mira / Omicron Ceti was a Federation system located in the Alpha Quadrant in the late 24th century.
A lost Federation colony on the fourth planet, Omicron Ceti IV, was seen in the comic book story Old Loyalties.