  Decay constants of pseudoscalar mesons $D$, $D_s$, $\eta_c$ and vector mesons
$D^*$, $D_s^*$, $J/\psi$ are determined from $N_f=2+1$ lattice QCD at a lattice
spacing $a\sim0.08$ fm. For vector mesons, the decay constants defined by
tensor currents are given in the $\overline{\rm MS}$ scheme at $2$ GeV. The
calculation is performed on domain wall fermion configurations generated by the
RBC-UKQCD Collaborations and the overlap fermion action is used for the valence
quarks. Comparing the current results with our previous ones at a coarser
lattice spacing $a\sim0.11$ fm gives us a better understanding of the
discretization error. We obtain $f_{D_s^*}^T(\overline{\rm MS},\text{2
GeV})/f_{D_s^*}=0.907(20)$ with a better precision than our previous result.
Combining our $f_{D_s^*}=277(11)$ MeV with the total width of $D_s^*$
determined in a recent work gives a branching fraction $4.26(52)\times10^{-5}$
for $D_s^*$ leptonic decay.
