Searching for a new thermoelectric (TE) material with a high figure of merit (ZT), at least 2.5, has a strong commercial motivation. Zintl phases are considered to be the most promising candidates for TE energy conversion through the recovery of waste heat. In the scope of the present research, we employed a combination of the first-principles calculations with Boltzmann transport theory to study the transport properties of two predicted compounds, SrIn2C2 and BaIn2C2, and compared the results with those of the previously synthesized MgAl2C2. We carried out geometric optimization for stable phase development and assessed their stability through various criteria, including formation enthalpies, reaction energy, decomposition energy, cohesive energy, and study of high-temperature stability via ab initio molecular dynamics calculations. Additionally, we investigate their dynamic stability via phonon dispersion and phonon density of states, indicating short phonon lifetimes, low phonon group velocities, and large scattering rates. The band gap values for MgAl2C2, SrIn2C2, and BaIn2C2 compounds are 2.46, 0.76, and 0.93 eV, respectively. It is noticeable that the total thermal conductivities (in the unit, W m-1 K-1) of MgAl2C2, SrIn2C2, and BaIn2C2 are 10.957, 1.538, and 0.383. The figures of merit of these three compounds at 300 K are 0.06, 0.19, and 1.10, respectively. The ultralow lattice thermal conductivity (0.24 W m-1 K-1) and high Seebeck coefficient (225 mu V K-1) at 300 K are the prime contributors to achieving the high ZT value of BaIn2C2. The unprecedented ZT value is 2.86 for BaIn2C2 and 1.93 for SrIn2C2 at a high temperature of 1000 K. Furthermore, the ductile nature and high melting point of BaIn2C2 render it highly suitable for practical applications.