  We present the differential predictions for the rapidity distribution of a
pair of leptons through the Drell-Yan (DY) process at the LHC taking into
account the soft-virtual (SV) as well as next-to-soft virtual (NSV) resummation
effects in QCD perturbation theory to next-to-next-to-leading-order plus
next-to-next-to-leading-logarithmic ($\rm{{NNLO+\overline{NNLL}}}$) accuracy.
We perform the resummation in two dimensional Mellin space using our recent
formalism \cite{Ajjath:2020lwb} by limiting ourselves to contributions only
from quark anti-quark ($q \bar q$) initiated channels. The resummed corrections
to the fixed order results are computed through a matched formula using the
minimal prescription procedure. We find that the resummation at
next-to-leading-logarithmic (next-to-next-to-leading-logarithmic) level brings
about 3.98\% (1.24\%) corrections respectively to the NLO (NNLO) results at the
central scale value of $q=M_Z$ for 13 TeV LHC. We also observe that the
sensitivity to the renormalisation scale gets improved substantially by the
inclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy.
Further, the lack of quark gluon ($qg$) initiated contributions to NSV part in
the $\rm \overline{NNLL}$ resummed predictions leaves large factorisation scale
dependence indicating their importance at NSV level as we go to higher orders
in perturbation theory.
