In this theoretical investigation, we delve into the significant effects of donor impurity position within core/shell quantum dot structures: type I (CdTe/ZnS) and type II (CdTe/CdS). The donor impurity’s precise location within both the core and the shell regions is explored to unveil its profound influence on the electronic properties of these nanostructures. Our study investigates the diamagnetic susceptibility and binding energy of the donor impurity while considering the presence of an external magnetic field. Moreover, the lattice mismatch-induced strain between the core and shell materials is carefully examined as it profoundly influences the electronic structure of the quantum dot system. Through detailed calculations, we analyze the strain effects on the conduction and valence bands, as well as the electron and hole energy spectrum within the core/shell quantum dots. The results highlight the significance of donor impurity position as a key factor in shaping the behaviors of impurity binding energy and diamagnetic susceptibility. Furthermore, our findings shed light on the potential for tuning the electronic properties of core/shell quantum dots through precise impurity positioning and strain engineering.