Sirius was the name of a binary star system in the Alpha Quadrant, located approximately nine light years from Sol. This inhabited planetary system was home to the stars Sirius A and Sirius B. (TNG: "The Naked Now" production art)
In 2293, the location of Sirius in the Milky Way Galaxy was labeled in the star chart "The Explored Galaxy", which was displayed in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In 2364, the location of Sirius A and Sirius B was labeled in a star chart of a stellar neighborhood with Sol at the center. This chart was stored in the USS Enterprise-D library computer. Later that year, the chart was scanned by Outpost 63. (TNG: "The Naked Now", production art; TNG: "The Last Outpost")
This system's quadrant of origin is inferred based on the position of neighboring locations – 61 Cygni, Alpha Centauri, Procyon, Sol, Tau Ceti, and Wolf 359 – as seen in the star charts appearing in the Star Trek: Discovery episode "Magic to Make the Sanest Man Go Mad" and in the Star Trek: Picard episode "Maps and Legends".
The Sirius group was mentioned in Gene Roddenberry's original Star Trek pitch in one of the suggested story lines. In the storyline "Kentucky, Kentucky," the Sirius group was home to an Earth colony for fifty years. This colony was attacked by Viking-like savages and reduced to a "frontier" log-fort life. They were regrouped and led by Captain Robert April when the SS Yorktown visited the colony.
The chart naming stars within twenty light years of Sol was originally drawn by Rick Sternbach for the Star Trek Spaceflight Chronology (p. 77) in the late 1970s. This chart showed Earth commercial and exploration routes after the use of warp drive began. Sirius was a destination on an exploration route.
According to Star Trek: Star Charts (pp. 45, 60, 66, "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Sirius (Alpha Canis Majoris) system was located in the Beta Quadrant. It was a binary star system with a pair of A-class stars. In the late 24th century, it was a Federation system.