Energy spectrum, wave functions and binding energies of the electron to the donor impurity ion located in the center of a multilayer spherical quantum dot (MSQD) consisting of a core (GaAs) and two spherical shells (AlxGa1–xAs and GaAs) were studied within the effective mass approximation. The magnetic field influence on the energy spectrum and wave functions of the electron is calculated by the diagonalization method. It is shown that the decrease of the external shell thickness as well as the increase of the magnetic field induction changes the electron localization in the nanosystem and it significantly affects the binding energy of the electron with the impurity, photoionization cross section (PCS) and intersubband absorption coefficient. The position of the PCS peak associated with the quantum transition of an electron from the ground state to the 1p0 state shifts to the region of higher energies, and its height decreases. At the same time, the height of PCS peaks associated with quantum transitions to higher excited states increases.