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We study the appearance of structures in the decay of the $B^-$ into $K^-\pi^- D_{s0}^+(2317)$ and $K^- \pi^- D_{s1}^+(2460)$ final states by forminginvariant mass distributions of $\pi^- D_{s0}^+$ and $\pi^- D_{s1}^+$ pairs,respectively. The structure in the distribution is associated to thekinematical triangle singularity that appears when the $B^- \to K^- K^{*\,0}D^0$ ($B^- \to K^- K^{*\,0} D^{*\,0}$) decay process is followed by the decayof the $K^{*\,0}$ into $\pi^- K^+$ and the subsequent rescattering of the $K^+D^0$ ($K^+ D^{*\,0}$) pair forming the $D_{s0}^+(2317)$ ($D_{s1}^+(2460)$)resonance. We find this type of non-resonant peaks at 2850 MeV in the invariantmass of $\pi^- D_{s0}$ pairs from $B^- \to K^- \pi^- D_{s0}^+(2317)$ decays andaround 3000 MeV in the invariant mass of $\pi^- D_{s1}^+$ pairs from $B^- \toK^- \pi^- D_{s1}^+(2460)$ decays. By employing the measured branching ratios ofthe $B^- \to K^- K^{*\,0} D^0$ and $B^- \to K^- K^{*\,0} D^{*\,0}$ decays, wepredict the branching ratios for the processes $B^-$ into $K^-\pi^-D_{s0}^+(2317)$ and $K^- \pi^- D_{s1}^+(2460)$, in the vicinity of thetriangle singularity peak, to be about $8\times10^{-6}$ and $1\times 10^{-6}$,respectively. The observation of this reaction would also give extra support tothe molecular picture of the $D_{s0}^+(2317)$ and $D_{s1}^+(2460)$.

Triangle singularities in $B^-\rightarrow K^-\pi^-D_{s0}^+$ and $B^-\rightarrow K^-\pi^-D_{s1}^+$