History and specifics
In the 23rd century, Ayin Aleph III was uninhabited, class M and suitable for colonization. It was nine light years away from the Lam Qaf Kha system and in the general vicinity of the Omicron Theta system.
In 2277, the USS Enterprise relocated descendants of the diminutive humanoid Tarachi civilization who survived the Second Great War on Omicron Theta V. Spock selected Ayin Aleph III as a suitable planet for them to colonize. (TOS - Star Trek II Short Stories short story: "The Secret Empire")