The next-to-minimal supersymmetric Standard Model with triplets is an attractive extension of the Standard Model. It combines the advantages of the next-to-minimal supersymmetric Standard Model and the minimal supersymmetric Standard Model with triplets to give three tiny Majorana neutrinos masses via a type-I+II seesaw mechanism. With the on-shell renormalization scheme, we consider the neutrino masses up to one loop approximation. Applying the effective Lagrangian method, we study the transition magnetic moments of Majorana neutrinos and consider the normal hierarchy and inverse hierarchy neutrino mass spectra within the constraints of experimental data on neutrino oscillations. The solar neutrino transition magnetic moment is further deduced, and compared with the XENONnT experiment limit. Published by the American Physical Society 2024