Joker Persona originally featured as a Persona under the control of JOKER during his first appearance. JOKER will continue to use this Persona until his eventual death at the hand of Tatsuya Suou.
During the time when Joker Curse spread, people who was infected by the Joker Curse gains ability to summon Joker Persona (or "degraded" variation of it) as their Persona. Those who already awaken their Persona and infected by Joker Curse will have their Persona overwritten by Joker as shown in the case of Ulala Serizawa.
In the added scenario included with the PSP version of Eternal Punishment, it is revealed by JOKER that the Joker persona was modeled after Tatsuya Suou.