\begin{document}$k_T$\end{document} factorization, we investigated the CP violation and branching ratios in the decay processes of \begin{document}$B_{c}^{+}\to D_{(s)} ^{+}V(V\rightarrow\pi^{+}\pi^{-})$\end{document} and \begin{document}$B_{c}^{+}\to D_{(s)}^{+}V(V\rightarrow K^{+}K^{-})$\end{document}, where V denotes the three vector mesons \begin{document}$\rho^0$\end{document}, ω, and ϕ. During the \begin{document}$V\to \pi^+\pi^-$\end{document} and \begin{document}$V\to K^+K^-$\end{document} decay processes, we incorporated the \begin{document}$\rho^{0}-\omega-\phi$\end{document} mixing mechanism to describe the amplitudes of these quasi-two-body decays. Within the interference region of the three vector particles, we observed distinct changes in both CP violations and branching ratios. Furthermore, our study presents evidence for local CP violations and branching ratios that warrants further experimental investigation."> CP violations and branching ratios for <i>B</i><sub><i>c</i></sub><sup>+</sup>→ <i>D</i><sub>(<i>s</i>)</sub><sup>+</sup><i>π</i><sup>+</sup><i>π</i><sup>−</sup>(<i>K</i><sup>+</sup><i>K</i><sup>−</sup>) from interference of the vector mesons in Perturbative QCD -
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