Controlling photon statistics is pivotal to many applications in classical and quantum photonics. While steady-state photon statistics have been widely studied, dynamically manipulating these statistical properties in time remains elusive. Herein, we propose a scheme to actively control photon statistics between bunching and antibunching regimes through quantum interference. Our approach relies on a Raman-coupled cavity-atom system with parametric amplification, where time modulating the detuning of the intermediate state allows us to either deepen the photon blockade or enhance photon bunching. Simultaneous modulation of the cavity and intermediate-state detunings produces antibunching that cannot be achieved under static conditions or by modulating either detuning alone. Because the modulation is periodic, the antibunching reappears at regular time intervals, enabling time-gated photon antibunching under continuous-wave operation at a repetition rate determined by the modulation frequency. These results show a versatile mechanism based on Raman-assisted quantum interference for dynamically engineering photon correlations.