As global uncertainty and trade tensions escalate, the world's economic stability faces growing risks. This study examines the volatility spillovers among economic policy uncertainty (EPU), energy, and carbon markets. We assume that returns in energy and carbon markets follow a Skew-t distribution and estimate volatility using an asymmetric EGARCH model. Then, we utilize methods developed by Diebold and Yilmaz (2012) and Barunik and Křehlík (2018), as well as a new quantile connectedness approach to investigate the directional and dynamic risk associations across different time frequencies and market environments. Our study first reveals that long-term volatility spillovers dominate normal periods, whereas medium-term spillovers become more pronounced in extreme cases. Second, EPU is a net receiver of risk in the short term but shifts to a risk transmitter in the medium and long term. Third, the solar energy market, a representative of new energy, drives spillover effects, while the carbon market is particularly susceptible to external influences. Fourth, the total risk spillovers exhibit a dynamic time-varying characteristic and are susceptible to extreme events. Finally, we observe an asymmetric distribution of risk spillovers among markets during extreme events. These findings offer valuable implications for policymakers and investors.