Abstract.: We study the partial decay widths of the charmonium states ( J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯, J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯, J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯, J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯, J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ to J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ (J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ or J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯) in isospin asymmetric nuclear matter, in the presence of strong magnetic fields. The in-medium partial decay widths of charmonium states to J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ are calculated within a light quark-antiquark pair creation model, namely the 3P0 model, using the in-medium masses of the charmonia as well as D and J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ mesons in the magnetized nuclear matter, obtained within a chiral effective model. The presence of a magnetic field leads to Landau quantization of the energy levels of the proton in the nuclear medium. The effects of magnetic field and isospin asymmetry on the charmonium decay widths to J/ψψ(3686)ψ(3770)χc0χc2DD¯D+D-D0D0¯DD¯D¯DD¯ are found to be quite prominent. The effects of the anomalous magnetic moments have also been taken into consideration for obtaining the in-medium masses of these heavy flavour mesons, used to calculate the partial decay widths of the charmonium states. The medium modifications of the charmonium decay widths can have observable consequences on the production of the charmed mesons in high energy asymmetric heavy ion collision experiments.