Located close to the Federation-Klingon border, Archanis IV was the fourth planet of the Archanis system in the Archanis sector. (TOS: "Day of the Dove"; DS9: "Broken Link")
In 2267, in the brief First Federation-Klingon War, a Federation research outpost was attacked by the Klingons. They massacred a hundred people.
A year later, while under the influence of the Beta XII-A entity, Pavel Chekov believed he had a brother, Piotr Chekov, who had been killed by the Klingons on Archanis. (TOS: "Day of the Dove")
Four years later, the Klingons relinquished their claim on this planet to the Federation. The Federation would eventually establish a colony on this planet. (DS9: "Broken Link")
Prior to the beginning of the Federation-Klingon War, Gowron sent a message to the Federation Council, telling them to remove all Starfleet forces from the planet and the system. The planet was soon taken over by the Klingons, although Starfleet would be regrouping for a counter-attack on the Archanis sector some months later. (DS9: "Broken Link", "Apocalypse Rising", "Nor the Battle to the Strong")
According to Startrek.com, Archanis Four was located in the Alpha Quadrant (the Archanis sector was adjacent to the Bajor sector). 
The fate of Archanis IV after the brief Federation-Klingon war ended in mid-2373 had not been mentioned on screen.
According to the Star Trek: Star Charts (pg. 62), in 2378, Archanis IV was a Federation member.