  A study of the $B^+\to K^0_SK^+K^-\pi^+$ and $B^+\to K^0_SK^+K^+\pi^-$ decays
is performed using proton-proton collisions at center-of-mass energies of 7, 8
and 13 TeV at the LHCb experiment. The $K^0_SK \pi$ invariant mass spectra from
both decay modes reveal a rich content of charmonium resonances. New precise
measurements of the $\eta_c$ and $\eta_c(2S)$ resonance parameters are
performed and branching fraction measurements are obtained for $B^+$ decays to
$\eta_c$, $J/\psi$, $\eta_c(2S)$ and $\chi_{c1}$ resonances. In particular, the
first observation and branching fraction measurement of $B^+ \to \chi_{c0} K^0
\pi^+$ is reported as well as first measurements of the $B^+\to K^0K^+K^-\pi^+$
and $B^+\to K^0K^+K^+\pi^-$ branching fractions. Dalitz plot analyses of
$\eta_c \to K^0_SK\pi$ and $\eta_c(2S) \to K^0_SK\pi$ decays are performed. A
new measurement of the amplitude and phase of the $K \pi$ $S$-wave as functions
of the $K \pi$ mass is performed, together with measurements of the
$K^*_0(1430)$, $K^*_0(1950)$ and $a_0(1700)$ parameters. Finally, the branching
fractions of $\chi_{c1}$ decays to $K^*$ resonances are also measured.
