The flow over wall-mounted circular cylinders is influenced by variations in aspect ratio, Reynolds number, and boundary layer thickness, all of which affect the vortical structures in the wake. In this study, we conducted direct numerical simulations and data-driven techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition, to examine vortical flows behind wall-mounted circular cylinders with aspect ratios of 4, 8, and 12 at Reynolds numbers ranging from 60 to 800, based on cylinder diameter. The incoming boundary layer thickness varied from 0.05 to 0.25. Our findings reveal that a thicker boundary layer promotes the development of low-frequency symmetric vortical structures along the wall surface, suppressing antisymmetric wake shedding. Consequently, the induced upwashing motion of the flow behind the cylinder pushes the wake shedding region closer to the free-end side, facilitating quadrupole mean streamwise vortices. The wake shedding frequency is significantly altered as the symmetric low-frequency mode intensifies along the boundary. POD analysis demonstrates the coexistence of symmetric and antisymmetric vortical structures in the wake region. The presence of either antisymmetric or symmetric wake shedding is determined by the dominant frequency in the instantaneous flow. These findings substantiate previous conjectures about the simultaneous presence of symmetric and antisymmetric wake shedding modes and enhance our understanding of vortical flows around wall-mounted circular cylinders.