A frontier world to which Harry Mudd claimed to be delivering three women as wives for lonely settlers when the Enterprise intercepted his ship.
Ophiucus III is a colony planet mentioned in the Original Series episode Mudd's Women.
After the Enterprise rescues Harcourt Fenton Mudd and his three passengers from a disintegrating cargo ship, Mudd is questioned at a hearing. He explains that he recruits wives for settlers and that Eve, Magda and Ruth were on their way to husbands on Ophiucus III.
The women never arrive. With the Enterprise's lithium crystals burnt out, the ship diverts to the mining station on Rigel XII, and Mudd arranges for the women to marry the miners there instead.