Betazoid space was a region of space in the Alpha Quadrant that contained Betazed and its outlying colonies; it was controlled by the Betazoids.
During the Dominion War, the Dominion invaded Betazed in 2374, approaching from the adjacent Kalandra sector. They managed to slip by both Starfleet Intelligence, who believed the area to be too far from the Dominion lines, and Tenth Fleet, who were out conducting training exercises. (DS9: "In the Pale Moonlight")
While apparently setting up for an invasion of nearby Vulcan later that year, the Dominion bolstered their hold on the Kalandra sector in order to further establish a supply line through Betazoid space into the Argolis Cluster. (DS9: "The Reckoning")
This region's quadrant of origin is inferred based on the position of Betazed as seen in the star chart appearing in the Star Trek: Picard episode "Maps and Legends".