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")
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 location of Altair III was labeled on a tactical situation monitor in Captain Benjamin Maxwell's ready room on the USS Phoenix. (TNG: "The Wounded", okudagram)
In 2366, in an alternate timeline, during the Federation-Klingon War, the location of Altair III was labeled on a tactical situation monitor in the ready room aboard the USS Enterprise-D (TNG: "Yesterday's Enterprise", okudagram)
In Gene Roddenberry and D.C. Fontana's final draft script of "Encounter at Farpoint", the planet was originally named Altair IV. 
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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