The molecular states in coupled channel system of Bₛ⁰N- BΛ- B^*Λ- BΣ- B^*Σ are investigated within one-boson-exchange model that includes S-D wave mixing and a tunable short-range δ(r) term. Bound, resonant, and virtual states are searched by analytically continuing the S matrix in the complex energy plane. In the single-channel analysis, the BΣ and B^*Σ systems with J^P=1/2⁻ and 3/2⁻ are found to be attractive and form three bound states with reasonable cutoff region, corresponding to 1/2⁻( BΣ), 1/2⁻( B^*Σ), and 3/2⁻( B^*Σ) . When coupled-channel dynamics is included, these states evolve into near-threshold poles that produce enhancements in the Bₛ⁰N, BΛ, and B^*Λ invariant mass spectra. The pole below the B^*Σ threshold in the J^P=1/2⁻ system depends strongly on the treatment of the short-range δ(r) term and becomes a virtual state when this contribution is removed, while the other two resonant poles and their line shapes are only moderately affected. For representative parameter region, the predicted masses of these states lie in the 6.44-6.52 GeV region and have widths of a few to several MeV. The pole coupling and partial-width analyses indicate that the poles are generated mainly by the BΣ and B^*Σ channels interaction, and their observable signals are expected mainly in the lower open channels Bₛ⁰N, BΛ, and B^*Λ. These results support the existence of near-threshold molecular pentaquark P_( b̄ s) and provide useful guidance in future experimental searches.