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We propose a next-to-minimal supersymmetric Standard Model (NMSSM) extendedby an $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ flavor symmetry and threeright-handed neutrinos providing a detailed study of the neutrino sector and asolution to the domain wall problem. In this proposal, neutrino masses aregenerated through Type I seesaw mechanism while the mixing angles are describedby the trimaximal mixing realized using the NMSSM singlet S and only two flavonfields. The phenomenology of neutrino parameters is studied for normal andinverted mass hierarchies. In particular, we numerically evaluated theobservables related to neutrino masses and mixing, namely, $\sum m_{i}$,$m_{ee}$, $m_{\nu_{e}}$, and $\delta_{CP}$ where we find that the ranges of$m_{ee}$ and $m_{\nu_{e}}$ are accessible by current and future experimentswhile the obtained ranges of $\sum m_{i}$ and $\delta_{CP}$ lie within thecurrent experimental data. Another attractive feature we discussed in thispaper is the circumvention of the domain wall problem induced by thespontaneous breaking of the $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ discretesymmetry. We first showed that the domain walls in the charged lepton sectoroccur at high energy scale leading to unproblematic domain walls, while in theneutrino sector they are inevitable. Then, to solve this problem, wereconsidered the well-known approach that relies on the explicit breaking ofthe discrete symmetry through the insertion of Planck-suppressed operatorsinduced by supergravity.  \keywords{Neutrino physics, Discrete flavor symmetry,Trimaximal mixing,Domain walls}

Neutrino phenomenology in the flavored NMSSM without domain wall problems