Aldebaran III was the inhabited third planet of the Aldebaran system. This planet was located near the Ficus sector. (TOS: "The Deadly Years"; TNG: "Up The Long Ladder", production art) The location of the Aldebaran system in the Milky Way Galaxy was depicted in the "The Explored Galaxy" star chart. (TNG: "Conspiracy", production art)
A few years prior to 2267, Janet and Theodore Wallace performed experiments using carbohydrate compounds to slow the aging of plants at the Federation outpost on this planet. (TOS: "The Deadly Years")
In "Conspiracy", the location of the Aldebaran system in the Milky Way Galaxy was depicted on a Federation star chart. On this chart, the star Aldebaran was positioned between the Tholian Assembly and Romulus. According to dialog in "Call to Arms", the two were Alpha Quadrant powers.
For the remastered edition of "Up The Long Ladder", the name Alderaan was changed to Aldebaran. It was not known if the diplomatic mission undertaken by the HMS New Zealand in 2135 was to this planet or to another planet in the system.
According to "Two Days and Two Nights", prior to 2151, Earth ships had been operating within 90 light years of the Sol system. In that year, the Enterprise became the first ship to travel further than this distance.
According to Startrek.com, this planet and Aldebaron III were the same. The planet was a Federation member.  According to the Star Trek: Star Charts ("United Federation of Planets I"), Aldebaran III (or Alpha Tauri III) was a Federation member in 2378.