This article investigates the dynamical effect of the dissipation forces, namely the Poynting-Robertson (PR) drag and nebular gas (Stokes) drag on the photogravitational magnetic-binary problem (PMBP) where the smaller primary is an oblate body and the bigger primary is the source of radiation. We have settled the equations of motion. The parametric evolution of the position and existence of equilibrium points and their linear stability are presented. Further, Newton-Raphson (N-R) basins of attraction have been plotted with the effect of Poynting-Robertson (PR) drag and nebular gas (Stokes) drag by Mathematica Software. Numerical results indicate that the ratio of magnetic moment λ has a significant impact on the location, stability of the equilibrium points, and the Newton-Raphson (N-R) basins of attraction of the problem. It is observed that there exist either nine or eleven equilibrium points for different values of mass parameter µ and the ratio of magnetic moment λ. Further, we observed that all equilibrium points are unstable in the Lyapunov sense. It is identified that in every case, the basins of convergence corresponding to the collinear equilibrium points L1 and L3 have infinite extents. Our numerical study suggests that the progression of the attracting domains in this dynamical system is very complicated. It is found that spacecraft is drifted from equilibrium points as a function of time due to instability of equilibrium points and drift is most for L7 point.