The first observations of
$B^0
ightarrowoverline{D}^{*}(2007)^{0}K^{+}pi^{-}$ and
$B_s^0
ightarrowoverline{D}^{*}(2007)^{0}K^{-}pi^{+}$ decays are presented,
and their branching fractions relative to that of the
$B^0
ightarrowoverline{D}^{*}(2007)^{0}pi^{+}pi^{-}$ 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 $B^{+}
ightarrow
DK^{+}$ and $B^{0}
ightarrow DK^{+}pi^{-}$ decays. The analysis is based on a
sample corresponding to an integrated luminosity of $5.4 ~
m{fb}^{-1}$ of
proton--proton collision data at $13 ~
m{TeV}$ 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 $overline{D}^{0}
ightarrow K^{+}pi^{-}$ 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.
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