- You may also be looking for Aldebaron III
Aldebaran III was the inhabited third planet of the Aldebaran system. This system was located in the Alpha Quadrant within 90 light years of the Sol system near the Ficus sector. (TOS: "The Deadly Years"; Star Trek VI: The Undiscovered Country production art; TNG: "Up The Long Ladder"; ENT: "Two Days and Two Nights")
In the star chart "The Explored Galaxy", the star Aldebaran was positioned between the Tholian Assembly and Romulus. Both were identified in DS9: "Call to Arms" as being located in the Alpha Quadrant. 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. With the diplomatic mission to Aldebaran in 2135, Aldebaran III was probably located within this range.
In the remastered "Up The Long Ladder", the HMS New Zealand was assigned to a diplomatic mission to Aldebaran. Captain Jean-Luc Picard asked for ...all Earth deep space launches...with a destination in or near the Ficus sector. The computer listed launches that, according to Commander William T. Riker, didn't end up in that sector. Presumably then, Aldebaran was located in a sector adjacent to Ficus.
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.