Sheridan was a star system located in the Organian Treaty Zone in the Alpha or Beta Quadrant, with at least three planets, including Sheridan's World, the only habitable planet in its system. Sheridan is located in an area of space at coordinates 8.49S, 0.0E. (FASA RPG module: Conflict of Interests)
This system obviously lies in one of the two quadrants that make up "local" space. However, since parts of the Federation and the Klingon Empire cross between the Alpha Quadrant and the Beta Quadrant, it is unclear where exactly the system is, since the FASA Corporation RPG was made years before the canon quadrant system was devised. There is a likelihood Sheridan system is in the Beta Quadrant, however, since that area houses the bulk of Klingon space.