Abstract <p>The aim of this paper is to investigate the motion properties of the infinitesimal variable mass body under the effects of gravitational forces of the primaries and the Poynting–Robertson drag. The equations of motion are determined for the above said perturbations along with those caused by the second primary having modified Newtonian potential. Utilizing these equations of motion, we analytically evaluate the equilibrium points and their stability as well as reveal the numerical study for potential surfaces, equilibrium points, basins of attractions and the stability of equilibrium points. This study presents useful insights for understanding the impact of various perturbations on the motion of small particles in a system and provides the impetus for innovative research in the field of dynamical astronomy and celestial mechanics.</p>