Vertically coupled quantum dots have emerged as promising structures for various applications such as single photon sources, entangled quantum pairs, quantum computation, and quantum cryptography. We start with a structure composed of two vertically coupled GaAs conical quantum dots surrounded by AlxGa1−x, and the effects of the applied electric and magnetic fields on the energies are evaluated using the finite element method. In addition, the effects are evaluated by including the presence of a shallow-donor impurity. The electron binding energy behavior is analyzed, and the effects on the photoionization cross-section are studied. Calculations are carried out in the effective mass and parabolic conduction band approximations. Our results show a notable dependence on the electric and magnetic fields applied to the photoionization cross-section. In general, it has been observed that both the electric and magnetic fields are useful parameters for inducing blueshifts of the resonant photoionization cross-section structure, which is accompanied by a drop in its magnitude.