Three-body hadronic B meson decays offer a rich environment for exploring the Standard Model and potential new physics. These decays are regularly interpreted in terms of the contribution of various scalar, vector and tensor resonant states. The investigation of appropriate decay processes will help us to comprehend the properties and substructures of the involved resonances. In relevant decay processes, the contributions from the tail of Breit-Wigner formula for the involved intermediate states have long been neglected in both theoretical and experimental investigations. In this work, we study the quasi-two-body decays B^+ \to \pi^+K^*0\to \pi^+K^0\eta^\prime, B^0 \to \pi^0 K^*0\to \pi^0 K^0\eta^\prime, B^0 \to K^0\barK^*0\to K^0\barK^0\eta^\prime and B_s^0 \to K^-K^*+ \to K^-K^+\eta^\prime within the perturbative QCD (PQCD) approach, where K^* denotes the resonances K^*(892) and K^*(1680). The corresponding three-body decays are currently under investigation by the LHCb and Belle-II experiments. Our analysis specifically focuses on the virtual contributions arising from the subprocess K^*(892)\to K\eta^\prime in these decay channels. The quasi-two-body framework based on PQCD approach has been discussed in detail in our former works. With the help of the effective weak Hamiltonian, the distribution amplitudes \phi_B for the B meson, \phi_h for the bachelor final state h and \phi_R for the resonance R, the decay amplitude \mathcalA for a quasi-two-body B decay expressed as the convolution \mathcalA=\phi_B\otimes H \otimes \phi_h\otimes \phi_R, where the hard kernel H contains only one hard gluon exchange at leading order. And then, Employing the decay amplitudes derived from the relevant Feynman diagrams for the concerned decay modes, we calculate the branching fractions and CP violations within the PQCD approach, the numerical results are found in the following Table. Our results are valuable for the understanding of various resonance contributions in the three-body B decays and are helpful for studying of the properties of the excited state K^*(1680). This work reveal very interesting and unique feature for the virtual contribution from the Breit-Wigner tail of the subprocess K^*(892)\to K\eta^\prime. As shown in the following figure for the differential branching fractions of the B_s^0 \to K^-K^*(892,1680)^+\to K^-K^+\eta' decays, the bump for the curve with K^*(892) is generated by the tail of the Breit-Wigner formula for the intermediate state along with the phase space factor. This feature should not be interpreted as evidence for a new resonant state around 2.0 GeV.