  A study of resonant structures in $B^{+}\rightarrow{D^{\ast+}D^{-}K^{+}}$ and
$B^{+}\rightarrow{D^{\ast-}D^{+}K^{+}}$ decays is performed, using
proton-proton collision data at centre-of-mass energies of $\sqrt{s}=7, 8$, and
$13$ TeV recorded by the LHCb experiment, corresponding to an integrated
luminosity of 9 fb$^{-1}$. A simultaneous amplitude fit is performed to the two
channels with contributions from resonances decaying to $D^{\ast-}D^{+}$ and
$D^{\ast+}D^{-}$ states linked by $C$ parity. This procedure allows the
$C$-parities of resonances in the $D^{\ast\pm}D^{\mp}$ mass spectra to be
determined. Four charmonium(-like) states are observed decaying into
$D^{\ast\pm}D^{\mp}$: $\eta_c(3945)$, $h_c(4000)$, $\chi_{c1}(4010)$ and
$h_c(4300)$, with quantum numbers $J^{PC}$ equal to $0^{-+}$, $1^{+-}$,
$1^{++}$ and $1^{+-}$, respectively. At least three of these states have not
been observed previously. In addition, the existence of the
$T_{\bar{c}\bar{s}0}^{*}(2870)^{0}$ and $T_{\bar{c}\bar{s}1}^{*}(2900)^{0}$
resonances in the $D^-K^+$ mass spectrum, already observed in the $B^+ \to D^+
D^- K^+$ decay, is confirmed in a different production channel.
