This paper combines quantile regression with time-varying vector autoregressive (TVP − VAR) model to study extreme spillover effects among high carbon emission stocks, green bond and WTI crude oil from April 21, 2010 to March 25, 2022. The results display a static total spillover index of approximately 49% at the conditional mean and conditional median estimates; while about 83% under the left tail and right tail estimates. The quantile-based spillover model is better than the mean-based one, because the former better captures the risk contagion mechanism under extreme market conditions. In addition, under extreme market conditions, green bond and WTI crude oil are net receivers of systemic shocks, while the remaining markets analyzed are net transmitters. The connectedness is time-varying in all cases, but the tail is less volatile. The analysis of relative tail dependence suggests the existence of asymmetric behavior, which implies different spillover effects in bullish and bearish markets. In addition, the European sovereign debt crisis has a much larger impact on spillovers under bearish markets than under bullish markets.