(covers information from several alternate timelines)
Altair III was an inhabited planet. It was the third planet of the Altair planetary system. The system was located in the Alpha Quadrant. This was one of three inhabited planets in this system; the others were Altair IV and Altair VI. (TOS: "Wolf in the Fold"; Star Trek VI: The Undiscovered Country, production art; 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")
The location of Altair III was depicted twice on the tactical situation monitor.
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. The Altair system, represented by Altair VI, was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in the Alpha Quadrant.This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game", and DS9: "In the Hands of the Prophets", "Cardassians".