Non-leptonic $B^0_s \rightarrow D_s^{\pm} K^{\mp}$ transitions are particularly interesting processes to test the Standard Model. As these decays occur via pure tree diagrams, they allow a theoretically clean determination of the angle $\gamma$ of the unitarity triangle. Considering recent LHCb results, an intriguing picture arises, showing tension with the Standard Model. Extracting the branching ratios of the underlying $\bar{B}^0_s \rightarrow D_s^{\pm} K^{\mp}$ modes and combining them with information from semileptonic $B_{(s)}$ decays, we arrive at another puzzling situation, in accordance with similar decays. These patterns could be footprints of New Physics. We present a model-independent strategy to include such New-Physics effects and apply it to the data. Interestingly, new contributions of moderate size could accommodate the data. This formalism offers an exciting probe for new sources of CP violation at the future high-precision B physics era.