(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The planet orbited a single star. During the Federation-Klingon War in 2267, James T. Kirk tried to warn the Organians that Klingons would move against their planet "as surely as your sun rises." (TOS: "Errand of Mercy")
In 2256, the location of Organia was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad", "The War Without, The War Within") (citation needed • edit)
In 2293, the location of Organia in the Milky Way Galaxy was labeled in the star chart "The Explored Galaxy", which was on display in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country okudagram)
In 2256, during the first Federation-Klingon War, the Organia system was occupied by the Klingons. This occupation lasted at least into the next year. (DIS: "Magic to Make the Sanest Man Go Mad", "The War Without, The War Within")
In the alternate reality, in the 2250s, Organia was a flashpoint between Federation and Klingon forces. In 2259, Starfleet was tracking the movement of Organian representatives in the San Francisco Metropolitan Area. Their current position was IDed by a label superimposed on a map of the area. This map was seen on a powerwall in the office of Christopher Pike at Starfleet Headquarters. (Star Trek Into Darkness)
In 2267, Organia was the only class M planet located in the disputed region of space between the Federation and Klingon Empire. Due to its strategic location, Organia became the focal point of the second Federation-Klingon War, which eventually led to its invasion by the Klingons, led by Commander Governor Kor. (TOS: "Errand of Mercy")
In its original appearance, Organia was represented with a generic planet model that was also used to depict other planets including Alfa 177, M-113, and Gothos. In the 2007 remastered version of "Errand of Mercy", Organia was represented by a unique, digital planet model.
In ultimately unused dialogue from the final draft script of ENT: "Observer Effect", Organia was described as being located far from Starfleet space as of 2154, and an Organian speculated that, at their present rate of exploration, Humans and Klingons would reach the planet in approximately a century.
According to Star Trek: Star Charts (pp. 54, 57 & 64) and Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography", p. 28, 30; "Federation Historical Highlights, 2161-2385"), Organia (Organia IV) was a quarantined planet in the late 24th century. The planet had no capital city, and the dominant species were the noncorporeal Organians. Not much was known to the Federation about the population, the official government, and if the Organians had become warp-capable and, if so, when. According to a map of the Klingon Empire – prepared by the Scribe K'Tark for the Klingon High Council in the Year of Kahless 893 (2266) – Organia was identified as a Klingon star. This claim was propagandistic, as the Empire claimed many border systems. This often put the Empire at odds with the Federation.