This research examines a novel hybrid energy system and analyzes its energy, exergy, environmental and economic aspects. The system employs a solid oxide fuel cell (SOFC) powered by methane and solar radiation to produce power, heat, and cooling-commonly referred to as Trigeneration. For the first time, a desiccant refrigeration system has been integrated with the fuel cell, utilizing the fuel cell's waste heat to regenerate the adsorbent material. The energy conservation equations are assessed for system components and resolved using EES software. The findings indicate that the electric power generated varied seasonally, producing approximately 1155 kW in spring and summer, and 1105 kW in autumn and winter, for a total of about 9903 MWh annually. The MOPSO approach was applied to optimize various objective functions, achieving an optimal configuration. The goals included enhancing exergy efficiency while minimizing power generation costs. The system's exergy efficiency was 78.2%, the fuel cell's exergy efficiency was 48.7%, and its energy efficiency was 47.5%. The exergy unit costs were determined to be 168.5 US$/GJ for the refrigeration load and 26.43 US$/GJ for electric power. According to the optimization outcome, the ideal quantity of SOFC cells is 11,000, with a steam-to-methane ratio of 2, optimal current density of 5,500 amperes per square meter, and an optimal temperature of 841 K for fuel and air entering the cell.