This paper employs the TVP-VAR-DY model to investigate the spillover among the European carbon market (EUA), the Chinese oil futures market (INE), and the Brent oil futures market (Brent) and explores whether their spillovers affect their volatility. Furthermore, we explore the impact of global uncertainties about the economy, finance, and geopolitics on their spillovers. The static analysis shows INE as a spillover receiver and EUA and Brent as transmitters. Dynamic analysis reveals spillover peaks during the COVID-19 pandemic. Furthermore, volatilities are positively influenced by spillovers...