Quasi-periodic oscillation (QPO) signals are discovered in some fast radio bursts (FRBs) such as FRB 20191221A, as well as in the X-ray burst associated with the galactic FRB from SGR 1935+2154. We revisit the intermediate-field FRB model where the radio waves are generated as fast-magnetosonic waves through magnetic reconnection near the light cylinder. The current sheet in the magnetar wind is compressed by a low frequency pulse emitted from the inner magnetosphere to trigger magnetic reconnection. By incorporating the wave dynamics of the magnetosphere, we demonstrate how the FRB frequency, the single pulse width, and luminosity are determined by the period, magnetic field, QPO frequency and quake energetics of the magnetar. We find that this model can naturally and self-consistently interpret the X-ray/radio event from SGR 1935+2154 and the QPO in FRB 20191221A. It can also explain the observed wide energy range of repeating FRBs in a narrow bandwidth.