  The first observations of
$B^0\rightarrow\overline{D}^{*}(2007)^{0}K^{+}\pi^{-}$ and
$B_s^0\rightarrow\overline{D}^{*}(2007)^{0}K^{-}\pi^{+}$ decays are presented,
and their branching fractions relative to that of the
$B^0\rightarrow\overline{D}^{*}(2007)^{0}\pi^{+}\pi^{-}$ decay are reported.
These modes can potentially be used to investigate the spectroscopy of charm
and charm-strange resonances and to determine the angle $\gamma$ of the CKM
unitarity triangle. It is also important to understand them as a source of
potential background in determinations of $\gamma$ from $B^{+}\rightarrow
DK^{+}$ and $B^{0}\rightarrow DK^{+}\pi^{-}$ decays. The analysis is based on a
sample corresponding to an integrated luminosity of $5.4 ~\rm{fb}^{-1}$ of
proton--proton collision data at $13 ~\rm{TeV}$ centre-of-mass energy recorded
with the LHCb detector. The $\overline{D}^{*}(2007)^{0}$ mesons are fully
reconstructed in the $\overline{D}^{0}\pi^{0}$ and $\overline{D}^{0}\gamma$
channels, with the $\overline{D}^{0} \rightarrow K^{+}\pi^{-}$ decay. A novel
weighting method is used to subtract background while simultaneously applying
an event-by-event efficiency correction to account for resonant structures in
the decays.
