We study the existence of charged fluid nonconducting structures orbiting in the background given by a Schwarzschild black hole immersed in a monopolelike magnetic field introduced in the context of the Blandford-Znajek process. Due to fact that the split-monopole magnetic field is not defined in the equatorial plane, where typical accretion disks are located, we focus on searching for off-equatorial charged toroidal structures. We demonstrate that charged nonconducting tori can arise very close to the symmetry axis of the magnetized black hole; thus representing a possible obstacle for jets created due to the Blanford-Znajek process.