This work investigates the quantum transport in a narrow constriction acted upon by a finite-range transversely polarized time-dependent field. A generalized scattering-matrix is developed that has incorporated a time-dependent mode-matching scheme. The transverse field induces coherent inelastic scatterings that include both intersubband and intersideband transitions. These scatterings give rise to the DC conductance G a general suppressed feature that escalates with the chemical potential. In addition, particular suppressed features - the dip structures - are found in G. These features are recognized as the quasibound state (QBS) features that arise from electrons making intersubband transitions to the vicinity of a subband bottom. For the case of larger field intensities, the QBS features that involve more photons are more evident. These QBS features are closely associated with the singular density of states at the subband threshold. An experimental setup is proposed for the observation of these features.