During the late 2350s, Galen IV was disputed between the Federation and the Talarian Republic, who saw the Federation as encroaching on their territory. In 2357, the planet was attacked during the Galen border conflict by Talarian forces, commanded by Endar. All the colonists were believed to have been massacred, the colony destroyed, but a single survivor emerged years later as Endar's adopted son Jono. (TNG: "Suddenly Human")
This planet was only mentioned in dialogue.
According to Star Trek: Star Charts (p. 37, "United Federation of Planets I", "United Federation of Planets III") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the primary of the Galen system was a K-class star. Galen IV was listed as a Federation member in 2378.