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   A study is presented of $B^{+}\to K_{\mathrm{S}}^0{K}^{-}{\pi }^{+}{K}^{+}$and $B^{+}\to K_{\mathrm{S}}^0{K}^{+}{\pi }^{-}{K}^{+}$decays based on the analysis of proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The $K_{\mathrm{S}}^{0}K\pi$invariant-mass distributions of both $B^{+}$decay modes show, in the $m\left(K_{\mathrm{S}}^{0}K\pi \right)<1.85\mathrm{GeV}$mass region, large activity which is resolved using an amplitude analysis. A simple model, where $J^{PC}$amplitudes are described by multiple Breit-Wigner functions with appropriate angular distributions, provides a good description of the experimental data. In this approach a complex mixture of $J^{PC}=0^{-+}$, $1^{++}$and $1^{+-}$amplitudes is observed that is dominated by $\eta \left(1405\right)$, $\eta \left(1470\right)$, $\eta \left(1760\right)$, $f_1\left(1285\right)$, $f_1\left(1420\right)$and $h_1\left(1405\right)$resonances. The $K_{\mathrm{S}}^{0}K\pi$Dalitz plots are dominated by asymmetric crossing $K^{*}\overline{K}$bands which are different for the two $B^{+}$decay modes. This is due to a different interference pattern between the $1^{++}$and $1^{+-}$amplitudes in the two channels. Branching fractions are measured for each resonant contribution. © 2025 CERN, for the LHCb Collaboration2025CERN 

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