According to Star Trek: Star Charts ("United Federation of Planets I"; "United Federation of Planets III") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Alpha system was located in the Alpha Quadrant. The primary was a G-class star. In 2378, Alpha III was listed as a Federation member.
According to Star Trek Maps (p. 22), the colony was established during the 22nd century as "Terra Four". By the 23rd century, the planet had a population of 175 million, it was a Federation member, and one of the seven members of the Federation security council.