  In-medium effects are introduced in the microscopic description of the
effective nucleon-nucleon (NN) interaction potential entitled DDR3Y in terms of
the density-dependent nucleon-meson couplings within the
Relativistic-Hartree-Bogoliubov (RHB) approach. The nuclear densities of the
interacting target and projectile nuclei and NN potentials are obtained for
non-linear NL3$^*$ and TM1 parameter sets within the relativistic mean-field
approach and density-dependent DDME1 and DDME2 parameter sets within the
Relativistic-Hartree-Bogoliubov (RHB) formalism. The DDR3Y NN potential and the
densities are used to obtain the nuclear potential by adopting the double
folding approach. This nuclear potential is further used to probe the fusion
dynamics within the $\ell-$summed Wong model for a few {\it even-even} systems
leading to the formation of light, heavy and superheavy nuclei. The
calculations are also performed for the relativistic R3Y, density-dependent and
independent M3Y interaction potentials for the comparison. We observed that the
DDR3Y NN potential gives a better overlap with the experimental data as
compared to non-relativistic M3Y and DDM3Y NN potentials. From the comparison
of R3Y and DDR3Y interactions, it is manifested that the inclusion of in-medium
effects in terms of density-dependent nucleon-meson couplings raises the fusion
barrier and consequently decreases the fusion and/or capture cross-section.
Moreover, the nuclear densities, as well as the relativistic R3Y NN potential
obtained for the NL3$^*$ parameter set, are observed to give a comparatively
better fit to the experimental data.
