The Onlies was the name that was taken by a group of feral children on Miri's homeworld following the spread of an artificial disease created from a life prolongation complex, which killing all adults on the planet in the 1950s.
The life prolongation project had indeed worked on the children and their life-spans were greatly increased. However, once they reached puberty, the children would contract the disease and eventually die.
For three centuries the surviving children banded together and scavenged amongst the abandoned cities, as well as playing games and supporting each other emotionally. When the USS Enterprise visited the planet in 2266, the onlies were distrustful of the "grups", following the madness that they experienced when the adults became insane centuries earlier.
Initially, the onlies attempted to drive the Enterprise landing party from the planet by attacking them (playing Foolies), stealing their communicators, and later kidnapping Yeoman Janice Rand. However, with the help of Miri, Captain James T. Kirk was able to win the children over. Following the Enterprise's departure, specialists from throughout the Federation traveled to the planet to care for and educate the onlies. (TOS episode & novelization: "Miri")