(covers information from several alternate timelines)
Antares was the primary of the Antares binary system. The secondary was Beta Antares. Antares sector was named after this system. This sector was a region of space in the Alpha Quadrant. (TOS: "The Conscience of the King"; TNG: "Conspiracy", display graphic; TNG: "The Wounded", display graphic)
The tactical situation monitor seen in "Yesterday's Enterprise" and "The Wounded" depicted Antares in the same region of space as the Altair system and Janus VI. According to "The Explored Galaxy" star chart, this region of space was located between the Tholian Assembly and Romulus. Both were identified in DS9: "Call to Arms" as being located in the Alpha Quadrant.
According to Star Trek: Star Charts ("United Federation of Planets II"), Antares (or Alpha Scorpii) was located in non-aligned space, in the Beta Quadrant. This was a binary star system. Antares A was a M-class star with a magnitude of -3, which was a thousand times brighter than Sol. Antares B was a B-class star.