  In this study, we work in the framework of the Next-to-Minimal extension of
the Standard Model (NMSSM) extended by six singlet leptonic superfields.
Through the mixing with the three doublet leptonic superfields, the non-zero
tiny neutrino masses can be generated through the inverse seesaw mechanism.
While $R$-parity is conserved in this model lepton number is explicitly
violated. We quantify the impact of the extended neutrino sector on the NMSSM
Higgs sector by computing the complete one-loop corrections with full momentum
dependence to the Higgs boson masses in a mixed on-shell-$\overline{\mbox{DR}}$
renormalization scheme, with and without the inclusion of CP violation. The
results are consistently combined with the dominant two-loop corrections at
${\cal O}(\alpha_t(\alpha_s+\alpha_t))$ to improve the predictions for the
Higgs mixing and the loop-corrected masses. In our numerical study we include
the constraints from the Higgs data, the neutrino oscillation data, the charged
lepton flavor-violating decays $l_i \to l_j + \gamma$, and the new physics
constraints from the oblique parameters $S,T,U$. We present in this context the
one-loop decay width for $l_i \to l_j + \gamma$. The loop-corrected Higgs boson
masses are included in the Fortran code NMSSMCALC-nuSS.
