(covers information from several alternate timelines)
The region of space, in which Sherman's Planet was located, was first mapped by astronomer John Burke in 2067. (TOS: "The Trouble with Tribbles", Star Trek Generations, display graphic; ENT: "In a Mirror, Darkly, Part II", display graphic)
In the alternate reality, Sherman's Planet was founded prior to 2259. On the eve of the founding in that year, there was a dispute about the Organian Peace Treaty. This dispute was reported in a news feed seen on a display graphic displayed in the office of Admiral Christopher Pike and the office of Admiral Alexander Marcus. (Star Trek Into Darkness, display graphic )
Following the Federation-Klingon War in 2267, and per terms of the Organian Peace Treaty, ownership of Sherman's Planet could be assumed by the side that could most effectively develop it. The Federation's intentions for Sherman's Planet were to use it to cultivate quadrotriticale, a grain well adapted to the planet's climate. After the quadrotriticale was poisoned on Deep Space Station K-7, Starfleet diverted a freighter laded down with this grain to Sherman's Planet. The grain would be delivered a few weeks later than anticipated. (TOS: "The Trouble with Tribbles")
The Federation succeeded in best developing Sherman's Planet. However, by 2269, the planet had been struck by famine. On Stardate 5392.4, the USS Enterprise, under Captain James T. Kirk, was assigned to escort two robot ships hauling an improved grain, quintotriticale, to the planet to alleviate the plight. (TAS: "More Tribbles, More Troubles")
According to Star Trek Maps (chart D), Sherman's Planet had six small moons called First, Second, Show, Last, Speed and Tiny one.
According to Star Trek: Star Charts (pgs. 53, 57, 62, "United Federation of Planets I"), Sherman's Planet was the fifth planet in the FGC-24187 system. The planet was located in or near Klingon space. It was M-class planet. Founded after 2267, the Sherman's Planet Joint Administrative Territory, the uniglobal government, had its seat in Port Emily, for the Federation, and in Ka'Hat, for the Klingons. There were counted 98.0 million humans and 116.2 million Klingons living on this world. This planet was on a disputed border with the UFP (2152-2267), and was settled according to the terms of the Organian Peace Treaty in 2267. In 2378, Sherman's Planet was a Federation member. FGC-24187 was a single star system with at least five planets. The star FCG-24187 was a G-class star with a magnitude of +1, which was a hundred times brighter than Sol.
In Star Trek Online, Deep Space K-7 is in orbit around Sherman's Planet.