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In 2020, China proposed the goal of achieving carbon emission peaks by 2030 and carbon neutrality by 2060. For China, whose energy consumption structure has long been dominated by fossil energy, carbon trading and new energy are crucial for the realization of the emission target. By establishing a connectedness network model, this paper studies the static and dynamic spillovers between the Hubei carbon trading market, new energy stock market, crude oil market, coal market, and natural gas market in China, and draws the following conclusions: (1) the static spillover index of the carbon–energy–stock system is 3.57% and the dynamic spillover index fluctuates between 7.67% and 22.62%, indicating that the spillover effect of the system is low; (2) for the whole system, whether from a static or dynamic perspective, the carbon market always plays the role of net information receiver, while new energy is the net information transmitter; (3) the new energy stock market and the coal market always act as net information transmitters to the carbon market; and (4) the spillover effect of the system is asymmetric, wherein the system is more sensitive to negative information about price returns, and this asymmetry is much greater when the system is active. [ABSTRACT FROM AUTHOR]