  The $\eta N$ interactions are investigated in the hot magnetized asymmetric
nuclear matter using chiral SU(3) model and chiral perturbation theory (ChPT).
In the chiral model, the in-medium properties of $\eta$-meson are calculated by
the medium modified scalar densities under the influence of an external
magnetic field. Further, in the combined approach of chiral model and ChPT,
off-shell contributions of $\eta N$ interactions are evaluated from the ChPT
effective $\eta N$ Lagrangian, and the in-medium effect of scalar densities are
incorporated from the chiral SU(3) model. We observe a significant effect of
magnetic field on the in-medium mass and optical potential of $\eta$ meson. We
observe a deeper mass-shift in the combined approach of ChPT and chiral model
compared to the effect of solo chiral SU(3) model. In both approaches, no
additional mass-shift is observed due to the uncharged nature of $\eta$ mesons
in the presence of magnetic field.
