Direct numerical simulation (DNS) is employed to investigate the wake dynamics of a circular cylinder positioned near a plane wall, subject to an unsteady approaching flow with an in-line oscillating component. This study is performed across three gap-to-diameter ratios ($G/D=1.0$, $0.5$, and $0.2$) at a Reynolds number of $Re=500$, an oscillation amplitude of $A/D=0.2$, and frequency ratios spanning $0<f_d/f_{st*}<3.0$. The resulting flow states are highly dependent on both wall proximity and forcing frequency. For lower gap ratio ($G/D=0.2$), vortex shedding is entirely suppressed at low frequencies, yielding to a single-row mode at higher frequencies. For larger gap ratios ($G/D=0.5$ and $1.0$), low-frequency forcing induces a “desynchronized” regime where vortex shedding remains independent of the inflow oscillation. At elevated frequencies, the flow enters a “locked-in” regime, synchronizing with the external forcing frequency $f_d$. The specific transitional pathways within this locked-in state are dictated by the gap size: the $G/D=0.5$ configuration features a direct transition from the A mode to the S mode, whereas the $G/D=1.0$ case undergoes intermediate mode competition, transitioning sequentially through the A mode, the Bimodal regime, and the S mode. The A mode exhibits an asymmetric topology with a $1/2$ subharmonic frequency response, where shedding vortices form clusters that convect and dissipate downstream. The S mode presents a quasi-symmetric pattern synchronized with the oscillation. The Bimodal regime serves as a transitional state where vortex shedding alternates between A and S modes. Furthermore, the results indicate that high-frequency oscillations effectively suppress the development of three-dimensional flow instabilities. Quantitative analysis using time-averaged spanwise kinetic energy spectra demonstrates that increasing the oscillation frequency effectively suppresses the three-dimensional instabilities in the near wake.