Within the framework of perturbative QCD factorization, we investigate the nonfactorizable contributions to the factorization-forbidden quasi-two-body decays   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   with   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $  . We compare our predicted branching ratios for the   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   decay with available experiment data as well as predictions by other theoretical studies. The branching ratios of these decays are consistent with data and other theoretical predictions. However, in the Cabibbo-suppressed decays   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   with   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $  , the values of the branching ratios are of the order of   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   and   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $  . The ratio   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   between the decays   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $     $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   and   $ B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-) $   and the distribution of branching ratios for different decay modes in invariant mass are considered in this study.