  We present first results on the resummation of Next-to-Soft Virtual (NSV)
logarithms for the threshold production of pseudoscalar Higgs boson through
gluon fusion at the LHC. These results are presented after resumming the NSV
logarithms of the kind ${\log}^{i}(1-z)$ to $\overline{\text{NNLL}}$ accuracy
and matching them systematically to the fixed order NNLO cross-sections. These
results are obtained using collinear factorization, renormalization group
invariance and recent developments in the NSV resummation techniques. The
phenomenological implications of these NSV resummed results for 13 TeV LHC are
studied and it is observed that these NSV logarithms are quite large. We also
evaluate theory uncertainties and find that the renormalization scale
uncertainties get reduced further with the inclusion of NSV corrections at
various orders in QCD. We further study the impact of QCD corrections on mixed
scalar-pseudoscalar states for different values of the mixing angle $\alpha$.
