The exceptional optoelectronic properties of quaternary chalcogenides have aroused a great deal of interest, especially for their potential application in most optoelectronic devices. Here, we investigated the diverse physical properties of novel BaQCuS3 (Q = Er and Gd) semiconductors by employing the density functional theory. The predicted band structures show that the compounds under investigation exhibit indirect band gaps. From the predicted density of states, the low energy levels of the Cu-d orbitals and their involvement in bonding and antibonding states with nearby atoms enable them to contribute to the valence band. The components of the complex dielectric function, absorption coefficients, real optical conductivity, energy loss functions, refractive index, reflectivity, and extinction coefficient, are also computed and explained to determine their potential usage in optoelectronic devices. We also calculated the thermoelectric transport parameters of these materials and discussed them in detail. The significant thermodynamic properties are also predicted to predict the stability of these compounds. The attained results in this work will have a substantial impact on the growth of effective integrated optoelectronic devices and the scope of their useful applications.