The Epsilon Outposts were a series of outposts constructed along the Federation side of the Federation-Klingon border. These outposts were located in the Beta Quadrant.
The location of each of the eleven outposts was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad")
In 2257, during the first Federation-Klingon War, all of these outposts were occupied by the Klingons. (DIS: "The War Without, The War Within")
This series of outposts was only mentioned in writing.
The name of these outposts came from the source material – the Star Trek: Star Charts (pp. 62-63) – used for the series' star charts. In the episodes, only the outposts' designation was mentioned.