The stability and half-metallic ferromagnetic properties of recently developed gapless semiconductor alloys, RhCoVZ (Z = Al, Ga, and In), were the subject of investigation in this research study. Three different non-equivalent structural configurations, namely type I, type II, and type III structures, have been examined. Among these compounds, Type I is characterized as the most stable phase in the ferromagnetic order, as opposed to the non-magnetic order. Through calculations of cohesive energies, formation energies, phonon dispersion curves, and elastic constants, we have demonstrated that RhCoVZ (Z = Al, Ga, and In) exhibits thermodynamic stability, as well as dynamic and mechanical. Using modified Becke-Johnson (mBJ) calculations, it has been revealed that RhCoVZ (Z = Al, Ga, and In) are spin gapless semiconductor half-metallic ferromagnets with an indirect bandgap. Additionally, it was observed that the electrons at the Fermi level (EF) are entirely spin-polarized. The total magnetic moment in all three compounds was determined to be an integer value of 2.00 µB per formula, in accordance with the Slater-Pauling rule (Mt = Zt - 24). All the calculations in this study were performed using density functional theory (DFT) based on the full-potential linearized augmented plane wave (FP-LAPW) method, which was implemented in the WIEN2k code. The effective mass of electrons/holes is (0.167/0.385) for RhCoVAl, (0.454/0.322) for RhCoVGa, and (0.604/0.242) for RhCoVIn. The thermoelectric properties of the three compounds were explored using the semi-classical Boltzmann transport theory. It was discovered that all three compounds exhibit high power factors and high Seebeck coefficients, with values reaching up to 1.5 mV/K for RhCoVAl and 1.25 mV/K for RhCoVGa. Based on the results, the highest observed ZT values for RhCoVZ (Z = Al, Ga, and In) are 0.95, 0.97, and 0.93, respectively. The study's findings indicate that these compounds possess stable characteristics, making them promising candidates for various device applications in fields like spintronics, thermoelectricity, shape memory, and spin filters. Furthermore, the investigation of their optical properties, including the dielectric function and absorption coefficient, suggests potential implications for optoelectronic applications. Overall, these materials exhibit diverse and valuable properties, opening up exciting opportunities for future technological advancements in multiple domains.