Multiple realities(covers information from several alternate timelines)
Altair III was the third planet in the Altair system. This system was located in Sector 9. (TOS: "Amok Time"; TNG: "Encounter at Farpoint") The location of the Altair system in the Milky Way Galaxy was depicted in the "The Explored Galaxy" star chart. (TNG: "Conspiracy", production art)
In the early 2360s, when the USS Hood visited this system, Lieutenant Commander William T. Riker refused to let Captain Robert DeSoto transport to the surface of Altair III with an away team because he deemed the action as too dangerous. By preventing his captain from beaming down, Riker disobeyed a direct order and risked a general court martial. (TNG: "Encounter at Farpoint", "The Pegasus")
In 2367, the planet appeared on a chart in Captain Benjamin Maxwell's ready room on the USS Phoenix. (TNG: "The Wounded" production art)
In an alternate 2366, Altair III was marked on a tactical situation monitor showing the fleet deployments in the Federation-Klingon War. (TNG: "Yesterday's Enterprise" production art)
The location of Altair VI, a sister planet of Altair III, on "The Explored Galaxy" wall chart
The location of Altair III on the tactical situation monitor
In Gene Roddenberry and D.C. Fontana's final draft script, the planet was originally named Altair IV. 
On the "The Explored Galaxy" chart, the Altair system was located between the Tholian Assembly and Romulus. According to dialog in "Call to Arms", the two were Alpha Quadrant powers.
According to the Star Trek: Star Charts (pg. 44), the Altair system, and Altair III, was located in or near Federation space, in the Alpha Quadrant.
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