  We present a measurement of the branching fractions of four $B^{0,-}\to
D^{(*)+,0} K^- K^{0}_S$ decay modes. The measurement is based on data from
SuperKEKB electron-positron collisions at the $\Upsilon(4S)$ resonance
collected with the Belle II detector and corresponding to an integrated
luminosity of ${362~\text{fb}^{-1}}$. The event yields are extracted from fits
to the distributions of the difference between expected and observed $B$ meson
energy to separate signal and background, and are efficiency-corrected as a
function of the invariant mass of the $K^-K_S^0$ system. We find the branching
fractions to be: \[ \text{B}(B^-\to D^0K^-K_S^0)=(1.89\pm 0.16\pm 0.10)\times
10^{-4}, \] \[ \text{B}(\overline B{}^0\to D^+K^-K_S^0)=(0.85\pm 0.11\pm
0.05)\times 10^{-4},\] \[ \text{B}(B^-\to D^{*0}K^-K_S^0)=(1.57\pm 0.27\pm
0.12)\times 10^{-4}, \] \[ \text{B}(\overline B{}^0\to D^{*+}K^-K_S^0)=(0.96\pm
0.18\pm 0.06)\times 10^{-4},\] where the first uncertainty is statistical and
the 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 $\overline
B{}^0\to D^{*+}K^-K_S^0$ decays and a significant improvement in the precision
of $\text{B}(B^-\to D^0K^-K_S^0)$ compared to previous measurements.
