N =3-extended supersymmetric Schwarzian and Liouville theories

N = 3 super-Schwarzian and N = (3, 0) super-Liouville theories are formulated by the coadjoint orbit method. We study the coadjoint orbit dependence of the respective theories, represented by a superfield b. We show that it is renormalized into the N = 3 super-Schwarzian derivative when the b field takes an appropriate configuration at the initial point of the orbit. Then the renormalized actions of the respective theories are invariant under OSp(2|3) transformations. If the configuration gets further specified, the initial point of the orbit turns out to be stable under one other kind of OSp(2|3) transformations as well.