The purpose of this paper is to study the motion properties of the third body which is moving inside the outer layer of the oblate heterogeneous body filled with the viscous fluid, under the influence of the oblate heterogeneous body and the radiating point mass which is producing the modified Newtonian potential. Wealso assume that the system is perturbed by the small perturbations in Coriolis and centrifugal forces. By using the evaluated system of equations of motion, we determine the locations of the collinear, non-collinear and out-of-plane equilibrium points. Finally, the stability examinations are done for these equilibrium points.