The efficient and sustainable exploitation of energy resources may secure a sustainable economic growth for different regions. However, the peripheries are subject to social, economic, and political constraints, with limited power over energy management. The present work examines regional convergence in exploitation efficiency as synopsized in the GDP generated by energy and minerals in an era of the country’s efforts to shut down the lignite-run power production. With the assistance of panel unit root tests, we confirm non convergence of the variables employed, an expected result given the fact that different energy sources are being used for energy production by each different periphery, generating different economic results. In the second stage the methodology employed is a Bayesian vector auto-regressive model (BVAR) with an informative prior on the steady state. The particular methodology outperforms the conventional VAR methodology due to limited degrees of freedom. The Impulse response analysis and the Variance Decomposition analysis confirmed interlinkages among the regions studied. This result implies that the growth generated by different energy and mineral resources are interconnected. Furthermore, the energy transition taking place in Megalopoli and West Macedonia, where the two greatest lignite industries were located until recently, affects the growth generated by energy and resource exploitation for all the other peripheries, according to our findings. The novelty of the present work stands on the concept to detect interlinkages of energy and resources-based growth for the peripheries in Greece with the assistance of the Bayesian Var. The results of the present work are significant, since our findings suggest to policy makers tools to promote economic growth generated by energy based on alternative energy sources, including the environmentally friendly ones, by taking into consideration the interlinkages established by the existing infrastructure and the conventional energy sources used.