This study investigates the dynamic relationship between the shift towards clean energy and stock market fluctuations, covering the period from January 2004 to August 2021 by applying time-varying parameters vector autoregressions (TVP-VAR). The results reported strong spillovers between clean energy markets and stocks, while dirty ones demonstrated disconnected spillovers. Asymmetry in the spillovers detected dominance of negative (bad) spillovers due to various uncertain economic and financial circumstances. The most significant negative (bad) events tracked in time-varying attributes are the global financial crisis, European Debt Crisis, Shale Oil Crisis, Brexit, US interest rate agenda, and the COVID-19 pandemic. Meanwhile, negative asymmetries prevailed in time-varying analysis, echoing the pre-eminence of negative crisis periods. We identified clean energy markets and stocks as net spillover emitters and dirty energy markets as net recipients. These findings have profound implications for a range of stakeholders, including investors, policymakers, and market participants, offering valuable insights for portfolio diversification and risk management strategies amidst the ongoing energy paradigm shift.