The court consists of the Fairy Judge, who resides over court, and the persecutor (as opposed to prosecutor) is Jorgen Von Strangle, who seems to muscle the judge around and thus has the true power in court.
In the episode "A Wish Too Far!", Timmy Turner and his fairies, Cosmo and Wanda, are brought here after Timmy overworks them while wishing for popular kid clothes and accessories without as much as a "thank you". At Fairy Court, Jorgen asks the judge to approach the bench, and then begins weight lifting off of an actual bench press with Cosmo spotting him. Cosmo is then allowed to cross-examine Timmy as his defense, but does a bad job and only gets Timmy in trouble.
Timmy tries to apologize, and the judge is about to let him go, but Jorgen threatens the judge with his wand, and the judge fearfully rules against Timmy. However, while Timmy is back on Earth, the judge and Timmy's fairies watch him perform an act of kindness toward Elmer, and decide to give Timmy another chance, although Jorgen forces a different punishment on Timmy: giving him a large boil on the side of his face.
Fairy Court is not seen again, although in a future Season 8 episode, Timmy is said to go on trial for being the "worst godkid ever", so it is extremely likely Fairy Court will reappear in the future.