The Theta VII colony was a Federation colony on the planet Theta VII.

In 2268, a disease caused a medical emergency here and vaccines were desperately needed. The USS Yorktown transported these vaccines and transferred them to the USS Enterprise, which then transported them to the colony. (TOS: "Obsession")

This colony was only mentioned in dialogue.
According to Star Trek Maps (p. 30), the Theta VII colony, established in 2147, was located on the only M class planet of the eleven planets that orbited the blue giant star Theta. The mining and farming colony was built underground to shield the inhabitants from solar flares. The colony had a population of 14,500.
According to Star Trek: Star Charts ("United Federation of Planets I"), in 2378, Theta VII was a Federation member.