The electron energy spectrum of a core/shell spherical quantum dot made of zincblende GaN/InN compounds is investigated taking into account the presence of an off-center donor atom and the influence of band nonparabolicity. The interaction of both the charge carrier and the Coulombic core with longitudinal optical phonons is included through Frö hlich and Aldrich-Bajaj theories, respectively. The ground state energy is determined by solving the resulting conduction band effective mass equation via the variational Ritz principle. A detailed analysis of the features of electron and hole spectra as functions of the core and shell sizes is presented, highlighting the possibility of transitioning between type-I and type-II structures. A detailed discussion about the effects of conduction band nonparabolicity, dielectric mismatch and electron-phonon interaction onto the impurity binding energy is provided. It was found that, in general, nonparabolicity of the conduction band leads to larger impurity binding energy, and that LO-phonon and dielectric mismatch effects tend to reduce the value of the latter quantity. © 2021, Springer-Verlag GmbH Germany, part of Springer Nature.