  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.
