A study of CP violation in $B^{\pm }\to D{K}^{\pm }$ and $B^{\pm }\to D{\pi }^{\pm }$ decays with $D\to K_{\mathrm{S}}^0{K}^{\pm }{\pi }^{\mp }$ final states

A first study of CP violation in the decay modes $B^\pm\to [K^0_{\rm S} K^\pm \pi^\mp]D h^\pm$and$B^\pm\to [K^0{\rm S} K^\mp \pi^\pm]_D h^\pm$,where$h$labelsa$K$or$\pi$mesonand$D$labelsa$D^0$or$\overline{D}^0$ meson, is performed. The analysis uses the LHCb data set collected in $pp$ collisions, corresponding to an integrated luminosity of 3 fb${}^{-1}$. The analysis is sensitive to the CP-violating CKM phase $\gamma$ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of $\gamma$ using other decay modes.