Measurement of $C\text{\hspace{0.17em}⁣}P$ asymmetries and branching-fraction ratios for $B^{\pm }\to D{K}^{\pm }$ and $D{\pi }^{\pm }$ with $D\to K_{\mathrm{S}}^0{K}^{\pm }{\pi }^{\mp }$ using Belle and Belle II data

We measure $C\text{\hspace{0.17em}⁣}P$ asymmetries and branching-fraction ratios for $B^{\pm }\to D{K}^{\pm }$ and $D{\pi }^{\pm }$ decays with $D\to K_{\mathrm{S}}^0{K}^{\pm }{\pi }^{\mp }$, where $D$ is a superposition of $D^0$ and ${\bar{D}}^0$. We use the full data set of the Belle experiment, containing $772\times {10}^{6}B\bar{B}$ pairs, and data from the Belle~II experiment, containing $387\times {10}^{6}B\bar{B}$ pairs, both collected in electron-positron collisions at the $\mathrm{{\rm Y}}(4S)$ resonance. Our results provide model-independent information on the unitarity triangle angle ${\phi }_3$.