In the final draft script of "Mudd's Women", references to this planet in the final version of that episode were instead to Ophiucus VI.
The Star Trek Encyclopedia (4th ed., vol. 2, p. 108) and StarTrek.com classified Ophiucus III as a class M planet. (The authors believed it was Ophiucus III which was mentioned in "Mudd's Women", not Ophiucus VI.)
An Earth colony was founded on this planet by the mid-22nd century. The colony was a destination on the Earth trade routes. In 2378, Ophiucus III was a Federation member. (p. 44, "United Federation of Planets I")
The Ophiucus System (or 36 Opiuchi System) was located in non-aligned space in the mid-22nd century. In 2378, this system was located in or near Federation space. This system was a quadrinary star system. Ophiucus A was a K-class star with a magnitude of +3, which was ten times brighter than Sol. Ophiucus B, Ophiucus C, and Ophiucus D were K-class stars. This system was the namesake for the Ophiucus Sector (Sector 008). (pp. 19, 44, "United Federation of Planets I")
The Ophiucus Sector (or Sector 008) was the eighth sector explored by Earth ships. (p. 19)