<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math> -wave contributions to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><…

We make a detailed study of the three-body decays ${B}_{(s)}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}h{h}^{\ensuremath{'}}$, where ${h}^{{(}^{\ensuremath{'}})}$ is either pion or kaon, by taking into account $S$-wave states in $h{h}^{\ensuremath{'}}$ invariant mass distribution within perturbative QCD approach. The two meson amplitudes are introduced to capture strong interaction related production system. calculate branching ratios for components and observe large values order ${10}^{\ensuremath{-}4}$ some Cabibbo-favored decays, which accessible LHCb Belle II experiments. obtained ratio $\mathcal{B}(B\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}{K}_{0}^{*}(1430)(\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}))=({5.1}_{\ensuremath{-}0.8}^{+0.6})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ consistent with data from errors. Moreover, we also predict differential distributions under consideration, await future experimental test. In addition, corresponding ${\ensuremath{\chi}}_{c1}(2P)$ channels investigated, helpful clarify nature $X(3872)$ state.