  In this article, we calculate the mass shift and decay constant of isospin
averaged pseudoscalar ($D^+$,$D^0$) and scalar ($D^+_0$,$D^0_0$) mesons by the
magnetic field induced quark and gluon condensates at finite density and
temperature of asymmetric nuclear matter. We have calculated the in-medium
chiral condensates from the chiral SU(3) mean field model and subsequently used
these condensates in QCD Sum Rules (QCDSR) to calculate the effective mass and
decay constant of $D$ mesons. Consideration of external magnetic field effects
in hot and dense nuclear matter lead to appreciable modification in the masses
and decay constants of $D$ mesons. Furthermore, we also studied the effective
decay width of higher charmonium states
($\psi(3686),\psi(3770),{{\chi_c}_0}(3414),{{\chi_c}_2}(3556)$) as a by-product
by using $^3P_0$ model which can have an important impact on the yield of
$J/\psi$ mesons. The results of present work will be helpful to understand the
experimental observables of the heavy ion colliders which aim to produce matter
at finite density and moderate temperature.
