The Morgana Quadrant was a region of space in the Alpha or Beta Quadrant.
By early 2365, this region had been explored by unmanned Federation ships.
In that year, the USS Enterprise-D was traveling to the Morgana Quadrant when it encountered the lifeform known as Nagilum during a star mapping mission. The Enterprise-D became the first manned Federation starship to chart this quadrant. (TNG: "The Child", "Where Silence Has Lease")
This term was used before the present system of four galactic quadrants was introduced in "The Price".
The author of the Star Trek: Star Charts (p. 15) stated that "prior to the mid-24th century, sector quads were commonly although mistakenly referred to as "quadrants"."