In this paper, we explore the linear, third-order nonlinear, and total optical absorption coefficient (OAC) and refractive index change coefficient (RICC) of a GaAs doped quantum dot/quantum ring (QD/QR) with parabolic-inverse squared potential in conjunction with modified Gaussian confinement and taking into account the presence of on-centre shallow donor and or acceptor impurity. Calculations are done via the compact density matrix formalism and the iterative method. The two-dimensional parabolic QD/QR is subjected to uniform magnetic field oriented perpendicularly to the plane of the structure. The energy levels and wave function are derived within the framework of effective-mass and parabolic band approximation. The results exhibit that the OACs and RICC are clearly affected by different parameters of the applied confinement, strength of magnetic field, and the presence of impurity. The variation of confinement potential, nature of impurity, dot radius, cyclotron frequency of the parabolic confinement potential, and geometric parameter of the on-centre repulsive potential lead to either a red-shift or a blue-shift of the resonant peaks of the OACs and of the maximum and minimum of the RICC together with significant variations of the magnitudes of these resonant structures.