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By adjusting the frequency of the cavity, we perform a microwave reflection measurement and directly probe the coherence and interference effects in a phase-sensitive Josephson parametric amplifier. We demonstrate the shift in the peak and the dip in the reflection spectra of the amplifier, which operates in the phase-sensitive mode. The behavior of the shift can be precisely controlled by tuning the pump power, the frequency of the cavity, and the relative phase between the incident signal and pump field. Theoretical simulations are in good agreement with the experimental results. These results provide an alternative way of controlling the parametric process by adjusting the frequency of the cavity.