We discuss how to calculate cross sections as well as rapidity, transverse momentum and energy distributions of ντ and {overline{nu}}_{tau } produced from the direct {D}_s^{pm}to {nu}_{tau }/{overline{nu}}_{tau } and chain {D}_s^{pm}to {tau}^{+}/{tau}^{-}to {nu}_{tau }/{overline{nu}}_{tau } decays in p+96 Mo scattering with proton beam Elab = 400 GeV i.e. at {sqrt{s}}_{NN} = 27.4 GeV. The τ decays are simulated with the help of the Tauola code and include multiple decay channels of τ in amounts proportional to their branching ratios. In our calculations we include {D}_s^{pm } from charm fragmentation c → {D}_s^{+} and overline{c}to {D}_s^{-} as well as those from subleading fragmentation of strange quarks/antiquarks s → {D}_s^{-} and overline{s}to {D}_s^{+} . The sne overline{s} asymmetry of the strange quark content of proton is included. The different contributions to {D}_s^{+} and {nu}_{tau }/{overline{nu}}_{tau } are shown explicitly. We discuss and quantify a not discussed so far effect of asymmetries for production of ντ and {overline{nu}}_{tau } caused by subleading fragmentation mechanism and discuss related uncertainties. A potential measurement of the asymmetry is discussed. Estimates of a number of observed {nu}_{tau }/{overline{nu}}_{tau } in the {nu}_{tau }/{overline{nu}}_{tau } +208Pb reaction, with 2m long target are given with the help of the NuWro program. We refer also to the production of the high-energy (anti)neutrinos in the atmosphere.