With the European Union's Artificial Intelligence Act taking effect on 1 August 2024, high-risk AI applications must adhere to stringent transparency and fairness standards. This paper addresses a crucial question: how can we scientifically audit algorithmic fairness? Current methods typically remain at the basic detection stage of auditing, without accounting for more complex scenarios. We propose a novel framework, ``peer-induced fairness'', which combines the strengths of counterfactual fairness and peer comparison strategy, creating a reliable and robust tool for auditing algorithmic fairness. Our framework is universal, adaptable to various domains, and capable of handling different levels of data quality, including skewed distributions. Moreover, it can distinguish whether adverse decisions result from algorithmic discrimination or inherent limitations of the subjects, thereby enhancing transparency. This framework can serve as both a self-assessment tool for AI developers and an external assessment tool for auditors to ensure compliance with the EU AI Act. We demonstrate its utility in small and medium-sized enterprises access to finance, uncovering significant unfairness-41.51% of micro-firms face discrimination compared to non-micro firms. These findings highlight the framework's potential for broader applications in ensuring equitable AI-driven decision-making.