The control of single dopant or ``solitary dopant'' in semiconductors constitute a challenge to achieve new range of tunable optoelectronic devices. Knowing that the properties of doped monocrystals are very sensitive to different external perturbations, the aim of this study is to understand the effect of a magnetic field on the ground state energy of an off-center ionized donor in a core/shell quantum dot (CSQD). The binding energies with and without an applied magnetic field are determined by the Ritz variational method taking into account the electron-impurity correlation in the trial wave function deduced from the second-order perturbation. It has been found that the external magnetic field affects strongly the binding energy, and its effect varies as a function of the core radius and the shell thickness. We have shown the existence of a threshold ratio (alb),i, which represents the limit between the tridimensional and the spherical surface confinement. In addition our analysis demonstrates the important influence of the position of ionized donor in the shell material.