The Beta Mahoga system was a planetary system which was located somewhere in the Alpha or Beta Quadrant.
In 2367, the USS Fearless was on a planetary mapping mission to this system. The system was mentioned in the chart "Starfleet Operations - Sectors 21166-23079" that was on display in the bridge of the USS Enterprise-D. (TNG: "Brothers" okudagram)
This system was only mentioned in writing.
In the Bayer designation, which was a system of stellar classification, the Greek letter indicated the brightness of a star in a constellation. In this case, Beta Mahoga would be the 2nd brightest star in its constellation.