  We investigate the in-medium masses of the pseudoscalar $(D,{\bar
D},D_s^{\pm})$, and vector $(D^*,\bar{D}^*, D_s^{*\pm})$, open charm mesons in
isospin asymmetric magnetized nuclear matter, accounting for the effects of
Dirac sea. The masses are used to study the in-medium partial decay widths of
$D^* \rightarrow D \pi$ ($\bar{D}^*\rightarrow \bar{D}\pi$) and $\Psi(3770)
\rightarrow D \bar{D}$, using the $^3P_0$ model. The in-medium masses of the
open charm mesons are calculated from their interactions with the nucleons and
scalar mesons within the generalized chiral effective model, in terms of the
scalar and number densities of nucleons and the scalar fields fluctuations. The
effects of Landau energy levels of protons and AMMs of the nucleons are also
considered in the magnetized nuclear matter. The light quark condensates are
modified considerably with magnetic field, leading to (inverse) magnetic
catalysis due to the magnetized Dirac sea effects. The magnetic field causes
modifications to occur due to the mixing of the pseudoscalar and longitudinal
component of the vector mesons, along with the lowest Landau level contribution
to the ground state energy of the charged mesons as point particle correction.
For the charmonium state $\Psi(3770)$, the effects of the magnetized Dirac sea
are incorporated to the mass modifications through the medium modified scalar
dilaton field $\chi$ within the chiral model. The in-medium masses and decay
widths of the open charm and charmonium mesons thus obtained should have
important observable consequences in the production of the open charm mesons
and charmonia in peripheral ultra-relativistic heavy ion collision experiments,
where huge magnetic fields are expected to be created.
