  We investigate the masses of the pseudoscalar ($D$($D^0$, $D^+$),
$\bar{D}$($\bar{D^0}$, $D^-$) and vector open charm mesons ($D^*$($D^{*0}$,
$D^{*+}$), ${\bar{D}}^*$(${\bar{D}}^{*0}$, $D^{*-}$) as well as the
pseudoscalar ($\eta_c(1S)$, $\eta_c(2S)$) and the vector charmonium states
($J/\psi$, $\psi(2S)$, $\psi(1D)$) in the asymmetric hot strange hadronic
medium in the presence of strong magnetic fields. In the magnetized medium, the
mass modification of open charm mesons due to their interactions with baryons
and the scalar fields ($\sigma$, $\zeta$, and $\delta$) are investigated in a
chiral effective model. Moreover, the charged pseudoscalar meson ($D^\pm$), as
well as the longitudinal component of charged vector meson ($D^{*\pm
\parallel}$), experience additional positive mass modifications in the magnetic
field due to Landau quantization. The effect of the modification of gluon
condensates simulated by the medium change of dilaton field $\chi$ on the
masses of the charmonia is also calculated in the chiral effective model. At
high temperatures, the magnetically induced modifications of scalar fields
significantly reduce the in-medium masses of mesons. The effects of
magnetically induced spin mixing between the pseudoscalar and the vector mesons
are incorporated in our study. The spin mixing result in a positive mass shift
for the longitudinal component of the vector mesons and a negative mass shift
for the pseudoscalar mesons in the presence of the magnetic field. From the
obtained in-medium mass shifts of charmonia and open charm mesons, we have also
calculated the partial decay widths of $\psi(1D)$ to $D\bar{D}$, using a light
quark pair creation model, namely the $^3P_0$ model. Spin mixing and
strangeness fraction enhance the partial decay width at small magnetic fields.
