In the presented paper, we introduce an analytical description for a dissipative two-mode parametric amplifier coherent cavity containing a three-level system (qutrit). Based on normalized correlation function, Q-function and its associated Wehrl entropy, the dynamics of the quantum phenomena: two-mode cavity non-classically, qutrit phase space information, and quantum coherence are investigated under the physical parameters: qutrit-cavity interactions, initial coherent intensity, and the dissipation. It is found that the generated quantum phenomena, due to the qutrit-cavity interaction, depend on the physical parameters of the initial states and the dissipation. The robustness of the quantum phenomena against the dissipation can be enhanced by decreasing the initial coherent intensity cavity. The stability and strength of the generated bunching/anti-bunching behaviour can be controlled by the cavity dissipation.