  The in-medium properties of $\eta$ mesons are studied in hot and dense
isospin asymmetric strange magnetized matter using the chiral SU(3) hadronic
mean-field model. The scalar and vector density of baryons are expressed in
terms of thermal distribution functions at finite temperature and magnetic
field and have dependence on the scalar fields $\sigma$, $\zeta$, and $\delta$
through the effective mass of baryons and the dependence on the vector fields
$\omega, \rho$, and $\phi$ through the effective chemical potential. The
properties of $\eta$ mesons get modified in a hot and dense magnetized
environment through the medium-modified nucleons and hyperons. The negative
mass shift obtained gives rise to optical potential, which is attractive in the
medium and suggests a possibility of $\eta$-mesic bound states formation. The
addition of hyperons in the medium enhances the attractive interactions and
causes an increased negative mass shift for $\eta$ mesons.
