The legend of Triacus stated that the planet was the homeworld for a band of marauders who were making constant war throughout the system of Epsilon Indi. After many centuries, these marauders were defeated by the very individuals who they preyed upon. The legend also mentioned that a powerful evil presence remained on Triacus, awaiting a catalyst to revive it, allowing it to spread its evil across the galaxy. This power was personified by Gorgan, the last of the planet's marauders.
In 2268, Triacus was the site of a scientific colony assembled by the Starnes Exploration Party, lead by Professor Starnes. On stardate 5038.3, one of the archeologists, Professor Wilkins, accidentally released Gorgan during an excavation of a cave near their encampment. It was noted that the destruction of whatever civilization that might have been there was produced by some natural catastrophe.
Gorgan influenced the children of the expedition and caused their parents to commit suicide. Gorgan made a further attempt, and was initially successful, to escape from Triacus aboard the USS Enterprise to spread its evil on to Marcos XII. (TOS: "And the Children Shall Lead")
In the 24th century, Lieutenant Commander Alexander Courage, a crewmember aboard the USS Enterprise-D, was born on this non-Federation planet. In 2369, his planet of origin was listed on the chart "USS Enterprise Personnel Database", which was displayed on a PADD accessed by Captain Jean-Luc Picard. (TNG: "The Chase", okudagram)
Based on the planet's seemingly close proximity to the Epsilon Indi system, it would seem that this planet is in, or is relatively near the Alpha Quadrant.