The Medusan homeworld was an inhabited planet and the homeworld of the non-corporeal Medusans.
In 2268, the USS Enterprise was assigned the mission of transporting Ambassador Kollos to his home. (TOS: "Is There in Truth No Beauty?")
According to The Worlds of the Federation, Medusa is the fourth planet in the Xi Hydrae system. It is called Visalayan by its natives. The Star Fleet Medical Reference Manual described it as the fifth planet in the Xi Hydrae system.
FASA's The Federation sourcebook described it as the fifth planet in the Rhys system.
Star Trek: The Original Series - Core Game Book referred to the planet as Medusa III.