Alpha III was the inhabited third planet of the Alpha system. The planet was the home of an Earth colony. An important piece of Human rights legislation, the Statutes of Alpha III, was written on this planet by the Tribunal of Alpha III. (TOS: "Court Martial")
Based on the statements of lawyer Samuel T. Cogley in "Court Martial", "Learn the intent of the men who wrote them, from Moses to the Tribunal of Alpha III?" and "Rights, sir, Human rights. The Bible, the Code of Hammurabi and of Justinian, Magna Carta, the Constitution of the United States, Fundamental Declarations of the Martian colonies, the Statutes of Alpha III.", Alpha III was colonized by Humans after the colonization of Mars.
According to Star Trek Maps (pg. 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. According to Star Trek: Star Charts ("United Federation of Planets I & III"), the Alpha system was a single star system in the Alpha Quadrant. Alpha was a G-class star with a magnitude of +5, the same brightness as Sol. Alpha III was a Federation member in 2378.