Here, we study the B s → D ( * ) s ℓν ℓ semileptonic decays within the Standard Model framework of covariant confined quark model. The necessary transition form factors are computed in the entire dynamical range of momentum transfer squared with built-in infrared confinement. Our computed ratios of the decay widths from tau mode to muon mode for D s and D * s mesons are found to be R(D s ) = 0.271 ± 0.069 and R(D * s ) = 0.240 ± 0.038. We further determine the ratio of the decay width from D s and D * s channel for muon mode Γ(B s → D s µ + ν µ )/Γ(B s → D * s µ + ν µ ) = 0.451±0.093. Our results are in excellent agreement with the data from recent LHCb experiments as well as lattice quantum chromodynamics simulations. We have also compared the shape of differential decay distribution for B s → D * s µ + ν µ with the recent LHCb data and our results are in very good agreement throughout all the individual bins. Some other physical observables such as forwardbackward asymmetry and longitudinal polarizations of leptons in the final state are also computed.