  An anomaly free non-universal $U(1)_{X}$ extension to the Minimal
Supersymmetric Standard Model is proposed, where additional two $SU(2)$ doublet
superfields and four singlet superfields complement the scalar sector of the
model. The fermion sector is extended by considering additional superfields
containing three quark singlets, two charged lepton singlet superfields and six
neutral leptons. A tree-level massless electron is found so radiative
corrections are considered to match the mass spectrum with both SUSY and
non-SUSY contributions. Likewise, a massless neutrino is found and analytic
expressions for massive mass eigenstates are obtained via inverse-seesaw
mechanism, which implies a known neutrino mass spectrum for both normal and
inverse ordering. Lastly, a numerical fitting of the model parameters to the
PMNS matrix is done.
