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We present a measurement of the branching fractions of four $B^{0,-}\toD^{(*)+,0} K^- K^{0}_S$ decay modes. The measurement is based on data fromSuperKEKB electron-positron collisions at the $\Upsilon(4S)$ resonancecollected with the Belle II detector and corresponding to an integratedluminosity of ${362~\text{fb}^{-1}}$. The event yields are extracted from fitsto the distributions of the difference between expected and observed $B$ mesonenergy to separate signal and background, and are efficiency-corrected as afunction of the invariant mass of the $K^-K_S^0$ system. We find the branchingfractions to be: \[ \text{B}(B^-\to D^0K^-K_S^0)=(1.89\pm 0.16\pm 0.10)\times10^{-4}, \] \[ \text{B}(\overline B{}^0\to D^+K^-K_S^0)=(0.85\pm 0.11\pm0.05)\times 10^{-4},\] \[ \text{B}(B^-\to D^{*0}K^-K_S^0)=(1.57\pm 0.27\pm0.12)\times 10^{-4}, \] \[ \text{B}(\overline B{}^0\to D^{*+}K^-K_S^0)=(0.96\pm0.18\pm 0.06)\times 10^{-4},\] where the first uncertainty is statistical andthe second systematic. These results include the first observation of$\overline B{}^0\to D^+K^-K_S^0$, $B^-\to D^{*0}K^-K_S^0$, and $\overlineB{}^0\to D^{*+}K^-K_S^0$ decays and a significant improvement in the precisionof $\text{B}(B^-\to D^0K^-K_S^0)$ compared to previous measurements.

Observation of ${B\to D^{(*)} K^- K^{0}_S}$ decays using the 2019-2022 Belle II data sample