  We analyze quasi-two-body charmless $B$ decays $B_{(s)} \to P_1 V \to P_1 P_2
P_3$ with $V$ representing a vector resonant, and $P_{1,2,3}$ as a light
pseudo-scalar meson, pion, kaon or $\eta^{(\prime)}$. The intermediate
processes $B_{(s)} \to P_1 V $ are calculated in the factorization-assisted
topological-amplitude approach and the vector resonant effects are described by
the Breit-Wigner propagator, which successively decay to $P_1 P_2$ via strong
interaction. Taking into account of all vector resonances in ground state,
$\rho, K^*, \omega, \phi$, we present the related branching fractions, and
calculate the virtual effects for $B_{(s)} \to \pi, K (\rho ,\omega \to) KK$.
We also predict direct $\it{CP}$ asymmetries of three body B decay modes with
$\rho, K^*$ resonances as intermediate states. Our predicted branching
fractions of decay modes dominated by the color-favored tree diagram or the
color-favored penguin diagram are consistent with the perturbative QCD
approach's predictions as well as QCD factorization approach. While for those
nonperturbative contribution dominated decay modes, the branching ratios in
this work are in better agreement with current experimental data than the PQCD
predictions and the QCD factorization results due to their shortage of the
nonperturbative contributions or $1/m_b$ power corrections. Many of the decays
channels, especially for direct $\it{CP}$ asymmetries, are waiting for the
future experiments.
