The decay widths of the charmonium states to $Dbar D$ in isospin asymmetric nuclear matter in the presence of a magnetic field are studied, using a field theoretical model for composite hadrons with quark/antiquark constituents. The medium modifications of these partial decay widths arise due to the changes in the masses of the decaying charmonium state and the produced $D$ and $bar D$ mesons in the magnetized hadronic matter, calculated within a chiral effective model. The decay widths are computed using the light quark--antiquark pair creation term of the free Dirac Hamiltonian in terms of the constituent quark field operators. The results of the present investigation are compared with the in-medium decay widths obtained within the $^3P_0$ model. Within the $^3P_0$ model, the charmonium decay widths are calculated using the creation of a light quark--antiquark pair in the $^3P_0$ state. In the presence of a magnetic field, the Landau level contributions give rise to positive shifts in the masses of the charged $D$ and $bar D$ mesons. This leads to the decay of charmonium to the charged $D^+ D^-$ to be suppressed as compared to the neutral $Dbar D$ pair in symmetric nuclear matter, whereas in asymmetric nuclear matter, the larger mass drop of the $D^+D^-$ pair, as compared to the $D^0 bar {D^0}$ pair leads to the production of charged open charm meson pairs to be enhanced as compared to the charmonium decay channel to $D^0 {bar {D^0}}$.
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