The greenhouse gas emissions from traditional fossil-fuel-based heating systems, particularly carbon dioxide, are a major environmental concern. To address these challenges and meet clean energy targets, this study proposes a sustainable, multi-generational energy system for a residential complex in Tabriz, Iran. The system integrates photovoltaic thermal panels, a high-efficiency biomass heater, a compact heat pump, and a power-to-gas unit with methanation to convert captured carbon dioxide into methane. Using TRNSYS for dynamic modeling, the photovoltaic thermal panels generate 230.94 MWh of electricity annually, with 53.4 % (123.3 MWh) allocated to immediate building demands and 38.9 % (89.9 MWh) used for hydrogen production. Peak carbon dioxide capture occurs in June at 778.23 kg, yielding 279.94 kg of methane, which enhances energy recycling and reduces emissions. System efficiency varies seasonally, reaching 51.35 % in winter, while the levelized cost of energy ranges from 100.08 $/MWh in June to 107.99 $/MWh in January. This approach demonstrates a cost-effective, environmentally friendly model for urban energy systems.