Earth Colony II was the site for a research base where James T. Kirk's brother "Sam" hoped to move with his wife Aurelan and their three sons when Kirk last saw him – at the departure of the USS Enterprise on her five-year mission in 2265.
In 2266, on Exo III, Captain Kirk tested Dr. Korby's android for precise knowledge of his personal history in the presence of Andrea, Nurse Chapel, and Korby: it knew that brother Sam hadn't said he would go to Colony II, but only that he "hoped to go" there. (TOS: "What Are Little Girls Made Of?")
In 2328, this was the point of embarkation for passengers traveling to the Tellun system via commercial transport. Mary Joy Macalintal, Michael Westmore, and Marion Westmore traveled there on the SS Kogin. (TNG-R: "Inheritance", okudagram)