<p>China’s coal-dominant energy structure faces growing supply-demand tensions and sustainability issues under the dual challenges of energy crisis and climate change. Existing studies have largely focused on the spatial heterogeneity of fossil energy consumption while paying insufficient attention to the characteristics of fossil energy supply itself, making it difficult to capture the intrinsic relationship between fossil energy supply and demand. Moreover, few studies have developed a comprehensive and dynamic index to evaluate the interactive balance of fossil energy supply and demand. To address this gap, this study innovatively developed the comprehensive supply-demand balance index (CSDBI) of fossil energy for Chinese provinces from 2004 to 2022 using the full permutation polygon synthetic indicator (FPPSI) method, and revealed their spatial heterogeneity and temporal variation characteristics from the perspectives of trend, stability, and persistence. The generalized additive model (GAM) was applied to identify primary socio-economic influencing factors of distinct fossil energy CSDBI clusters. The results indicate that the CSDBI generally presented a distribution pattern of deficit (0 ~ 0.64) in southern provinces and surplus (0.65 ~ 1) in northern provinces. The changing trend of CSDBI shows a situation of weakening in the east and strengthening in the west. The future evolution of fossil energy supply-demand pattern demonstrates relatively strong persistence, with provinces experiencing persistent decline predominantly located in coastal regions, whereas those showing persistent increase are mainly concentrated in the northwest. The driving mechanisms of different CSDBI clusters are markedly heterogeneous, both in the composition of socio-economic factors and in the cluster-specific nature of their effects. High-surplus clusters, mainly composed of major fossil energy-supply provinces in the north and west, benefit from rich resources and low local demand, resulting in strong self-sufficiency and export capacity. In contrast, moderate-deficit clusters face local supply shortfalls despite possessing some resource base, while high-deficit clusters, whether in less-developed inland or advanced coastal regions, suffer from severe resource scarcity and strained supply-demand balance. Urbanization level is the dominant factor of high-deficit and moderate-deficit clusters, while industrial structure plays a more important role in the high-surplus cluster. Based on above findings, high-surplus provinces should promote quality-oriented industrial upgrading and cleaner energy development while restraining energy-intensive expansion. Moderate-deficit provinces should better align urbanization with energy-structure optimization through technological upgrading, industrial greening, and renewable substitution. High-deficit provinces should combine compact urban development with energy-efficiency improvement and consumption-structure optimization to alleviate long-term supply-demand pressure. The proposed study advances a novel spatial-temporal analytical framework for understanding fossil energy supply-demand evolution, provides a new theoretical perspective to quantify regional fossil energy supply-demand matching, and offers scientific support for nations to address the global energy crisis and facilitate energy market equilibrium.</p>