This article presents a theoretical study of the nonlinear electronic, impurity, and optical properties of CdS/ZnS quantum dots subjected to the simultaneous effects of electric and magnetic fields. The magnetic field is considered along the axial axis ($z$-axis) with the donor impurity always located in the center of the quantum dot. In the case of the applied electric field, for both situations of radial and axial field the azimuthal symmetry of the system is preserved. In the absence of a magnetic field and considering a radial field, the system retains spherical symmetry both in the presence and absence of the impurity. The study is carried out in the effective mass approximation and using the finite element method to find the eigenfunctions and their corresponding energies both in the presence and absence of the impurity. For the study of the analyzed optical properties, optical absorption coefficient and coefficient of changes in the refractive index, the transitions between states with $l=0$ (which have azimuthal symmetry) are considered, taking transitions from the ground state to the first fourteen excited states and considering incident radiation with linear polarization along the $z$-axis. This study shows that the presence of the radial electric field can give rise to a core/shell system where ground state oscillations appear in the presence of the applied magnetic field. Additionally, it is shown that the presence of the donor impurity suppresses such oscillations and that it is responsible for blue shifts in the optical properties and increases in the magnitudes of the corresponding resonant structures.