The location of Omega Cygni on "The Explored Galaxy" wall chart
Omega Cygni was an inhabited planet. This was the homeworld for the Omega Cygni natives, an intelligent species. The planet was located in the Alpha Quadrant. Its location in the Milky Way Galaxy was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
Prior to stardate 4978, Harry Mudd visited Omega Cygni, where he turned a handsome profit selling the natives their own oceans. (TAS: "Mudd's Passion")
Background
Omega Cygni was misspelled "Omega Cyngi" on "The Explored Galaxy" star chart. "The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Omega Cygni was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. The chart, first seen chronologically in Star Trek VI: The Undiscovered Country, was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game", and DS9: "In the Hands of the Prophets", "Cardassians".
Apocrypha
According to the Alan Dean Foster novelization of TAS: "The Time Trap" in Star Trek Log 4 and Star Trek: SCE, Magen was a Cygnian from Omega Cygni. In the novelization of "Mudd's Passion" in Star Trek Log 3, the name "Omega VII" was used of this planet.
The novels Beneath the Raptor's Wing and Synthesis suggest that Omega Cygni was related to Cygnet XIV.