Through quantum electrodynamics (QED) we investigate the interactions between a three-level atom and two photon fields under perturbation limit. The dispersion relation and (relative) transmission of the probe photons are obtained by calculating the corresponding Feynman diagrams. The quantum interference in this three-level system such as Fano resonance and electromagnetically induced transparency (EIT) can be tuned by varying the intensities of the control and probe beams. Moreover, by considering that the control beam with periodic modulation, that is, the so-called Landau-Zener-Stückelberg (LZS) type source, the accumulated phase after Landau-Zener transitions is found to show the alternating Fano (EIT) lineshapes in the transmission of the probe photons. We further find that the transmissions can become almost stationary in addition to a wide EIT window in time even though the control beam is a LZS-type oscillating source.