We give a detailed study of ground state properties, magnetism, mechanical, thermoelectric, thermodynamic, and optical properties of rare-earth-based quaternary Heusler YFeMnAl and YFeMnGa alloys using the DFT and post-DFT methods. The structure optimizations, display the LiMgPdSn-type structure as stable phase with F-43 m symmetry. The spin-polarized band structure shows the alloys as perfect half-metallics with indirect band gap of 0.364 eV in YFeMnAl and 0.391 eV in YFeMnGa. The magnetism also supports their half-metallic character with an integral value of 3.00 mu B estimated using the Slater-Pauling curve rule. Mechanical stability is calculated using the elastic constants which define their ductile nature. Transport coefficients are investigated to see their capability as green energy sources where thermopower "S" measurements at room temperature are -29 mu VK-1 for YFeMnAl and -9 mu VK-1 for YFeMnGa, with negative sign displaying their n-type majority heat carriers. Conversion efficiency of these materials descripts the figure of merit as 0.22 for YFeMnAl and 0.86 for YFeMnGa, respectively. The thermodynamic parameters like the heat capacity, Debye temperature, Gruneisen parameter, thermal expansion coefficient, and volume against pressure and temperature are sued to infer their stability at extreme conditions.