Ophiucus VI was the inhabited sixth planet of the Ophiucus system.

In the mid-23rd century, Harry Mudd visited Ophiucus VI, where he conned two miners out of a year's supply of dilithium crystals using fake Federation vouchers. (TAS: "Mudd's Passion")

This planet was only mentioned in dialogue.
Ophiucus VI was an early name for the planet which became Ophiucus III. As such, Ophiucus VI was repeatedly referred to in the final draft script of TOS: "Mudd's Women". In the novelization of "Mudd's Passion" (as published in Star Trek Log 3), Harry Mudd referred to this planet as a "charming frontier world."
According to Star Trek: Star Charts (pp. 18, 19, & 44; "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Ophiucus (36 Ophiuchi) system was located in the Ophiucus sector (Sector 008), in the Beta Quadrant.