The Morgana Quadrant was a region of space.
The USS Enterprise-D was traveling to the Morgana Quadrant when it encountered the lifeform known as Nagilum in 2365 during a star-mapping mission. The Enterprise-D was the first crewed 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 non-canon book Star Trek: Star Charts states that sector quadrants are sometimes referred to as quadrants.