In 2364, the location of Epsilon Eridani 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 star was only mentioned in writing.
The chart naming stars within twenty light years of Sol was 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. Epsilon Eridani was the destination for two major commercial routes, Alpha Centauri-Epsilon Eridani and Sol-Epsilon Eridani.
According to Star Trek: Star Charts (p. 66) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Epsilon Eridani (Axanar) star system was located in the Beta Quadrant. The inhabited planet Axanar (the Axanar homeworld) was located in this system. The binary system had two K-class stars.
Epsilon Eridani has, on occasion, been misidentified as Vulcan's sun. In 1991, Star Trek creator Gene Roddenberry, along with three scientists from the Harvard-Smithsonian Center for Astrophysics, instead endorsed 40 Eridani A for the location of the Vulcan system. Their rationale was that, since Epsilon Eridani is less than a billion years old, "life on any planet around Epsilon Eridani would not have had time to evolve beyond the level of bacteria. On the other hand, an intelligent civilization could have evolved over the aeons on a planet circling 40 Eridani. So the latter is the more likely Vulcan sun."