We investigate hadronic molecular states with the quark contents $ccqq\overline{s}$, $bbqq\overline{s}$, and $bcqq\overline{s}$ ($q=u$, $d$) by employing the extended local hidden gauge approach. Considering that the $S$-wave meson-baryon interactions are dominated by vector meson exchange, the coupled channels scattering amplitudes are obtained by solving the Bethe-Salpeter equation in its on-shell form. We find that the poles appearing on the complex Riemann sheet are potential candidates for dynamically generated molecular pentaquark states. The results suggest the existence of a total of fourteen molecular states with quantum numbers $I(J^P)=0(1/2^{-})$, $0(3/2^{-})$, and $0(5/2^{-})$, which arise from the interactions of the $K^{(*)}{\mathrm{\Xi }}_{cc}^{(*)}$, $K^{(*)}{\mathrm{\Xi }}_{bb}^{(*)}$, $K^{(*)}{\mathrm{\Xi }}_{bc}^{(*)}$, and $K^{(*)}{\mathrm{\Xi }}_{bc}^{\prime }$ channels, respectively. Their binding energies are calculated to be about 0.1–33 MeV, and this range depends on the free parameter of the theory. Our research contributes to the spectroscopic studies of hadronic molecular pentaquark states.

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• Bethe-Salpeter equation
• Multiquark bound states
• Particle interactions
• Phenomenology
• Scattering amplitudes