  The medium modifications of the masses of the charmonium states (J/$\psi$,
$\psi$(3686) and $\psi$(3770)) in asymmetric nuclear matter in the presence of
strong magnetic fields are studied using an effective chiral model. The mass
modifications arise due to medium modifications of the scalar dilaton field,
which simulates the gluon condensates of QCD within the effective hadronic
model. The effects due to the magnetic field as well as isospin asymmetry are
observed to be appreciable at high densities for the charmonium states, which
can have consequences, e,g, in the production of the open charm mesons and the
charmonium states, in the asymmetric heavy ion collisions at the compressed
baryonic matter (CBM) experiments at the future facility at GSI. The presence
of magnetic field leads to Landau quantization of the energy levels of the
proton in the asymmetric nuclear matter. The effects of the anomalous magnetic
moments of the proton and neutron on the masses of the charmonium states are
studied and are observed to lead to larger masses of the charmonium states, as
compared to when these effects are not taken into account.
