This study explores links between uncertainty metrics and fossil and green energy sectors, applying an innovative quantile-on-quantile connectedness method to analyze spillovers across quantiles from August 2004 to December 2023. Our sample comprises the clean and fossil energy market indices and key uncertainty measures, including climate, economic, geopolitical, and infectious diseases uncertainty indices. All total connectedness indices were found to peak at extremely reversely related quantiles, except for climate policy uncertainty. The strongest connectedness is between high economic policy uncertainty and low clean energy returns. The economic policy uncertainty index was dynamically reversely related to energy markets in all quantiles. However, after 2016, the connectedness between climate policy uncertainty and energy market indices converted to positive, possibly due to the impact of the Paris Agreement. Compared to climate-related uncertainty, geopolitical and economic uncertainties have a notably more substantial influence on energy markets, particularly in the green energy sector. Other findings reveal that energy market performance significantly influences climate policy uncertainty, and that infectious disease uncertainty is transmitted across various quantiles. Given the findings, we propose policy implications for investors and policymakers, emphasizing the critical need for considering different quantiles in measuring the dynamic connectedness between various uncertainties and energy markets.