In this work, we conduct an investigation on the optical emission properties of a pumped-dissipative QD-cavity system within the Lindblad master equation approach, where the cavity mode is modeled through the R-deformed realization of the Heisenberg algebra (RDHA). We found that the parity deformation parameter associated with the RDHA gives rise to a collective phenomenon by reordering the one-photon optical transitions of the system, and it is demonstrated that there are two critical values for this parameter where a new type of spectral triplet arises in the emission spectrum. Moreover, our results reveal that depending on the critical value of the deformation parameter, the spectral triplets observed in the emission spectrum exhibit signatures of the weak- and strong-coupling regimes simultaneously.