Miridian VI was the sixth planet in the Miridian planetary system. This uninhabited planet was located in Federation space near the Romulan Neutral Zone.
When Barash posed as the Human boy Ethan on Alpha Onias III in 2367, he claimed to have been captured by Romulans during an attack on a Federation outpost on Miridian VI. Commander Riker was surprised to hear about this outpost as he had no knowledge about it (which ultimately turned out to be true). (TNG: "Future Imperfect")
Miridian VI appeared in the starchart Data and Picard were studying in Stellar Cartography in 2371. (Star Trek Generations)
According to the Star Trek: Star Charts (pages 61,66), the Barradis system was located in the Beta Quadrant. This system was a single star system. Primary was a Class K star with a magnitude of +5, which was the same brightness as Sol. In the mid-22nd century, this system was in or near Romulan space. After 2160, this system was in or near Federation space.