In this article, we aim to prioritize barriers hindering sustainability inclusion within clean energy supply chains. Supply chain management is a crucial aspect of the clean energy sector, whereby the global supply chains can be enforced with policies to adopt sustainability/green practices. The literature infers that the adoption of sustainability is not direct, and multiple barriers impede the process, driving researchers to rank these barriers. Previous studies on prioritizing barriers cannot effectively model uncertainty; experts' reliability is directly assigned; interrelationships/hesitation of criteria/experts are usually not considered; and there is a lack of personalized ordering based on individuals' preferences. Motivated by these gaps, the authors put forward an integrated framework with a Fermatean fuzzy set, variance-based criteria importance through intercriteria correlation for determining experts' and criteria weights, and ranking procedure with complex proportional assessment-Copeland for personalized ordering of barriers. The usefulness of the developed approach is testified through a case example. Results infer that wastage/pollution reduction and profit from green production are the two top criteria considered for rating sustainability barriers, while limited governmental policies, monitoring/control issues, and expertise mismatch are the top three barriers impeding sustainability adoption. Finally, sensitivity and comparative analyses are performed to understand the framework's efficacy.