Xianxia or Murim?
The first strives to become immortal with impeccable beauty and unrivaled supernatural powers. The second describes the world of martial artists, while they have internal power sometimes also called qi, they are not immortal, age normal, and have some fancy attacks but not on the scale of nuclear bombs.
Both judge people internally in their realm. They exist beside the normal folks, but because mortals die with one of their slaps, the normie judge court can’t handle them.
Normally the family clan, sect, or master they belong to will oversee and correct their wrongdoings. As for the what punishment there are, it’s ranges from being grounded at home, to doing manual labor to reflect to being exiled and executed.