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Equilibrium configurations of electrically charged perfect fluid surrounding a central rotating black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Following our previous studies considering the central black hole non-rotating, we show that in the rotating case, conditions for the configurations existence change according to the spin of the black hole. We focus our attention on the charged fluid in rigid rotation which can form toroidal configurations centered in the equatorial plane or the ones hovering above the black hole, along the symmetry axis. We conclude that a non-zero value of spin changes the existence conditions and the morphology of the solutions significantly. In the case of fast rotation, the morphology of the structures is close to an oblate shape., Comment: 12 pages, 10 figures