Some time prior to 2265, a young James T. Kirk and Gary Mitchell came to this planet, where Mitchell got involved with a woman. Kirk later stated that he'd been worried about Mitchell ever since that night, and Mitchell referred to the girl as a Nova, a pun suggesting the danger he had been in.
Also during the 23rd century, inhabitants of Deneb IV communicated telepathically. In at least three cases during the 2260s, Gary Mitchell carried on long telepathic conversations with select Deneb IV natives and scored eighty percent or higher on comprehension. (TOS: "Where No Man Has Gone Before")
By 2364, the Bandi had seemingly constructed Farpoint Station, a base which they subsequently offered to Starfleet. Intrigued by the extremely short time in which it was built, Starfleet sent the USS Enterprise-D on its maiden voyage to the planet in order to investigate the base. It was subsequently discovered that the station was in fact a spaceborne entity, enslaved by the Bandi. Upon this discovery, the entity was released, and Starfleet and the Bandi began planning to reconstruct the station. (TNG: "Encounter at Farpoint")
Behind the Scenes
Michael Okuda recalled how Deneb IV was originally depicted in "Encounter at Farpoint"; "The beautiful shot of Deneb IV was actually a matte painting done by Industrial Light & Magic, and that was done on film." Speaking shortly before the release of Star Trek: The Next Generation - The Next Level Blu-Ray sampler, Okuda also compared the remastered version of the planet with the original, saying, "The planet is pretty much dead on with what was done in the original shot."  He was referring to the planetary shot of Deneb IV in this interview.
The planet surface of Deneb IV, including Farpoint Station and Bandi city, was in actuality a maquette, built by maquette specialist Gregory Jein. It, combined with a background matte painting, was filmed at ILM by visual effects cameraman Robert Hill. (The Official Star Trek: The Next Generation Magazine, issue 2, January 1988, p. 41)
The Explored Galaxy
This chart was first seen, chronologically, in 2293. (Star Trek VI: The Undiscovered Country) This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
The author, Geoffrey Mandel, believed that there were two planets that shared the same name. The two planets were Deneb IV (Deneb Kaitos IV (Beta Ceti IV)) and Deneb IV (Alpha Cygni IV).
Deneb IV (Deneb Kaitos IV (Beta Ceti IV))
Deneb IV (Deneb Kaitos IV (Beta Ceti IV)) was located in the Alpha Quadrant. This planet was a Class M planet. It was a Federation member world. In the mid-22nd century, this planet's system was named as a stop on the Vulcan trade routes.
Deneb IV (Alpha Cygni IV)
Deneb IV (Alpha Cygni IV) was located in the Alpha Quadrant. Located 3,230 light years from Sol, this planet was a Class M planet. The official name of this planet was Bandi. Deneb IV was first an affiliate of the Federation after signing a treaty in 2364, than became a member by 2378. The capital of Deneb IV was Farpoint. The dominant species of the planet were the humanoid Bandi. In 2378, there were an estimated 450 million Bandi living on the planet. Major points of interest were Farpoint Station and Old City. Under the terms of the Treaty of 2364, Starfleet operated Starbase Farpoint Station.
(Pages 33, 34, 41, United Federation of Planets I)