<p>China's dual-carbon strategy has led to more significant emission reduction goals, prompting a thorough examination of dynamic interplay among carbon-energy markets. By scrutinizing spillovers across carbon-energy markets as China refines its carbon trading system, this will enable a comprehensive understanding of carbon-energy system information transmission. An analysis of time-varying risk spillover effects is carried out using China's pilot carbon market, traditional energy markets, power market, and new energy market, employing Generalized Autoregressive Conditional Heteroskedasticity, Skewness and Kurtosis model, Diebold-Yilmaz models. Results indicate the overall time-varying spillover index of various moments fluctuates significantly among carbon-energy markets. Compared with the stable return rate spillover index, the volatility, skewness and kurtosis indices exhibit sharper jumps with more drastic variations, particularly in higher-order moments. The application of the rolling window method exposes time-varying attributes among markets and regional variations in the impact of fluctuations on individual carbon markets. Results further confirmed that the carbon-energy system is susceptible to risks primarily originating from shock periods in the traditional energy market. There is a prevalent belief that promoting a more rapid integration of markets, along with enhancing the price mechanism, risk prevention, and early warning systems, is crucial. Moreover, to mitigate the impact of external conditions-induced risk spillovers, the development mechanism for each carbon market should be tailored to regional distinct features.</p>