Alpha III

From Memory Alpha, the free Star Trek reference

Alpha III is a planet famous for being the site where the Statutes of Alpha III were written. It was home to the well-known Tribunal of Alpha III, who wrote important laws such as the Statutes. (TOS: "Court Martial")

Given that Samuel T. Cogley cited the Statutes as a legal precedent, it is more than likely that Alpha III is a Federation member world. We don't exactly know what star this planet orbits, as there are innumerable stars whose name contains "alpha," making it unlikely that this would orbit a star "Alpha" (as astronomical naming conventions suggest based on the "Alpha III" notation). It is possible this was a reference to a commonly mentioned system, such as Alpha Centauri. See Alpha system for more information.