We investigate the process $$B\rightarrow \bar{D}D_s \pi $$ B → D ¯ D s π via several rescattering processes. It is shown that the triangle singularity (TS) peak around the $$D^*K^*$$ D ∗ K ∗ threshold generated from the $$\chi _{c1}K^* D^*$$ χ c 1 K ∗ D ∗ loop is relatively narrow, which may simulate the resonance-like structure $$T_{c\bar{s}}(2900)$$ T c s ¯ ( 2900 ) recently observed by LHCb in the $$D_s\pi $$ D s π spectrum. However, the TS peak around the $$D_s^*\rho $$ D s ∗ ρ threshold generated from the $$D^{**} D_s^* \rho $$ D ∗ ∗ D s ∗ ρ loop is smoothed by the broad width of $$\rho $$ ρ , which itself can hardly describe the $$T_{c\bar{s}}(2900)$$ T c s ¯ ( 2900 ) structure. A non-resonance TS signal around the DK threshold generated from the $$\chi _{c0}K D $$ χ c 0 K D loop is also predicted.

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In this work, we propose to search for the exotic doubly charmed meson $$T_{cc}^+$$ T cc + and its analog $$T_{cc\bar{s}}^+$$ T c c s ¯ + in $$B_c^+$$ B c + decays, which provide a good environment for the formation of the exotic state containing double charm quarks. Within the molecular scheme, the production of $$T_{cc}^+$$ T cc + and $$T_{cc\bar{s}}^+$$ T c c s ¯ + through various rescattering processes with different intermediate states are investigated. For the moderate values of model parameters, the branching ratios of $$B_c^+$$ B c + decaying into $$T_{cc}^+ \bar{D}^{0}$$ T cc + D ¯ 0 , $$T_{cc}^+ \bar{D}^{*0}$$ T cc + D ¯ ∗ 0 , $$T_{cc\bar{s}}^+ \bar{D}^{0}$$ T c c s ¯ + D ¯ 0 and $$T_{cc\bar{s}}^+ \bar{D}^{*0}$$ T c c s ¯ + D ¯ ∗ 0 are estimated to be of the order of $$10^{-7}$$ 10 - 7 , $$10^{-5}$$ 10 - 5 , $$10^{-6}$$ 10 - 6 and $$10^{-4}$$ 10 - 4 , respectively, which may be tested by future experiments.

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