We investigate the returns connectedness between 118 energy firms of 10 of the most relevant countries on energy consumption, and the natural gas and oil prices for the period between January 3, 2006 and December 15, 2023. Based on a novel combination of the quantile connectedness and spillover decomposition approaches, our results demonstrate that the natural gas, oil and energy stock markets are closely interconnected, mainly in bearish and bullish scenarios. Almost a quarter of the total spillover at the country-level comes from the interaction between stock and fuel markets, but such contribution is reduced to less than 4% when the network is configured at firm-level. Energy stock markets of the United States, Canada, Italy, Spain and the United Kingdom are the main shocks transmitters, while Japan and China are net receivers within the global energy network. Oil and natural gas can be important alternatives for risk diversification, mainly in medium and low return scenarios. We also identify the most and least vulnerable energy sectors and firms in the entire network in each scenario, establishing precise recommendations for the design of energy policies and investment decision-making.