The Caldonians are an interesting species that only appeared in the TNG episode, “The Price“. They have large craniums, and are expert researchers who would prefer to avoid administrative duties and simply focus on scientific investigation. In 2366, they were interested in the Barzan wormhole, but Devinoni Ral was able to persuade them to abandon their bid, by emphasizing how much of a bureaucratic nightmare the wormhole administration would prove to be.
It is unlikely that they were members of the Federation in 2366, but you may of course add them to the Federation after that in your own campaign, should you so wish. Also, any individual Caldonian may have sought Federation citizenship, and could have applied to Starfleet.