  We investigate the mass-shift of $P$-wave charmonium (${\chi_c}_0$,
${\chi_c}_1$) and $S$ and $P$-wave bottomonium ($\eta_b$, $\Upsilon$,
${\chi_b}_0$ and ${\chi_b}_1$) states in magnetized hot asymmetric nuclear
matter using the unification of QCD sum rules (QCDSR) and chiral $SU(3)$ model.
Within QCDSR, we use two approaches, $i.e.$, moment sum rule and Borel sum
rule. The magnetic field induced scalar gluon condensate $\left\langle
\frac{\alpha_{s}}{\pi} G^a_{\mu\nu} {G^a}^{\mu\nu} \right\rangle$ and the
twist-2 gluon operator $\left\langle \frac{\alpha_{s}}{\pi} G^a_{\mu\sigma}
{{G^a}_\nu}^{\sigma} \right\rangle $ calculated in chiral $SU(3$) model are
utilised in QCD sum rules to calculate the in-medium mass-shift of above
mesons. The attractive mass-shift of these mesons is observed which is more
sensitive to magnetic field in high density regime for charmonium, but less for
bottomonium. These results may be helpful to understand the decay of higher
quarkonium states to the lower quarkonium states in asymmetric heavy ion
collision experiments.
