  We investigate the in-medium masses of open charm mesons ($D$($D^0$, $D^+$),
$\bar{D}$($\bar{D^0}$, $D^-$), $D_s$(${D_{s}}^+$, ${D_{s}}^-$)) and charmonium
states ($J/\psi$, $\psi(3686)$, $\psi(3770)$, $\chi_{c0}$, $\chi_{c2}$) in
strongly magnetized isospin asymmetric strange hadronic matter using a chiral
effective model. In the presence of the magnetic field, the number density and
scalar density of charged baryons have contributions from Landau energy levels.
The mass modifications of open charm mesons arise due to their interactions
with nucleons, hyperons, and the scalar fields (the non-strange field $\sigma$,
strange field $\zeta$ and isovector field $\delta$) in the presence of the
magnetic field. The mass modifications of the charmonium states arise from the
variation of dilaton field ($\chi$) in the magnetized medium, which simulates
the gluon condensates of QCD. The in-medium mass of open charm mesons and
charmonia are observed to decrease with an increase in baryon density, whereas
the charged $D^+$, $D^-$, ${D_{s}}^+$ and ${D_{s}}^-$ mesons have additional
positive mass shifts due to Landau quantization in the presence of the magnetic
field. The effects of strangeness fraction are found to be more dominant for
the $\bar{D}$ mesons as compared to the $D$ mesons. The mass shifts of
charmonia are observed to be larger in hyperonic medium compared to the nuclear
medium.
