The regime created on Ekos by the Federation historian John Gill in imitation of Nazi Germany, which under Deputy Führer Melakon turned to the persecution and planned destruction of the Zeons.
The Ekosian Nazi Party is the government found by the Enterprise in the Original Series episode Patterns of Force. John Gill, a historian sent as a cultural observer, broke the Prime Directive by giving the divided Ekosians a state copied from Nazi Germany, which he believed had been the most efficient in Earth's history.
Gill intended to keep the efficiency and leave out the cruelty. Instead his deputy Melakon kept him drugged, ruled in his name as Führer and directed the party's hatred at the Zeons, launching a campaign he called the final solution.
Not every member is loyal: the party chairman Eneg and the honoured Daras secretly work with the underground. After Gill's dying broadcast and Melakon's death, Eneg takes charge and promises to undo the damage.