<p>The structural, electronic, magnetic, thermal, and optical properties of the quaternary Heusler alloys FeCrTiM (where M = Al, As, Si) were investigated using first-principles density functional theory (DFT) calculations. The ground state is found to be the type-1 ferrimagnetic configuration. In addition, the calculated formation energies (− 1.63 eV for FeCrTiAl, − 1.048 eV for FeCrTiAs, and − 0.774 eV for FeCrTiSi) confirm that these compounds are thermodynamically stable relative to their elemental constituents<b>,</b> suggesting the possibility of experimental synthesis under suitable conditions. The calculated lattice constants and ground-state parameters for FeCrTiAs and FeCrTiAl are presented as theoretical predictions. Based on band structure analysis, FeCrTiAs and FeCrTiSi exhibit half-metallic ferrimagnetism at equilibrium, although near spin-gapless features may emerge under lattice distortions. This makes them promising candidates for spintronic applications. All studied compounds display half-metallic ferrimagnetism with total magnetic moments that follow the Slater-Pauling rule, increasing linearly with the number of valence electrons. The optical properties reveal high static dielectric constants and refractive indices, indicating potential applications in optoelectronic devices. Additionally, the thermoelectric performance of these materials was evaluated, with calculated Seebeck coefficients up to ~ 1.5 mV·K⁻¹, electrical conductivity σ ≈ 3.5 × 10⁶ S·m⁻¹, electronic thermal conductivity around 25 W·m⁻¹·K⁻¹, and a predicted figure of merit (ZT) close to 1 at 300 K. These combined results suggest that FeCrTiM (M = Al, As, Si) alloys are multifunctional materials with strong potential for use in high-performance energy conversion, optoelectronics, and spintronic devices.</p>