In characterizing the chiral phase-structure of pseudoscalars ($J^{pc}=0^{-+}$), scalars ($J^{pc}=0^{++}$), vectors ($J^{pc}=1^{--}$) and axial-vectors ($J^{pc}=1^{++}$) meson states and their dependence on temperature, chemical potential, and magnetic fields, we utilize SU($3$) Polyakov linear-sigma model (PLSM) in mean-field approximation. We first determine the chiral (non)strange quark condensates, $sigma_l$ and $sigma_s$ and the corresponding deconfinement order parameters, $phi$ and $phi^*$, respectively, in thermal and dense (finite chemical potential) medium and finite magnetic field. The temperature and the chemical potential characteristics of nonet meson states normalized to the lowest {it bosonic} Matsubara frequencies are analyzed. We noticed that all normalized meson masses become temperature independent at different {it critical} temperatures. We observe that the chiral and deconfinement phase transitions are shifted to lower {it quasicritical} temperatures with increasing chemical potential and magnetic field. Thus, we conclude that the magnetic field seems to have almost the same effect as that of the chemical potential, especially on accelerating the phase transition, i.e. inverse magnetic catalysis. We also find that increasing chemical potential enhances the mass degeneracy of the various meson masses, while increasing the magnetic field seems to reduce the critical chemical potential, at which the chiral phase transition takes place. Our mass spectrum calculations agree well with the recent PDG compilations and PNJL, lattice QCD calculations, and QMD/UrQMD simulations.
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