As the healthcare sector highly adopts blockchain to enhance data security and patient data integrity, it becomes imperative to create robust authentication system. This paper provides the formal modeling and verification of blockchain-based authentication System specifically designed for the healthcare sector, using Event B. With the high integration of blockchain in healthcare sector to bolster data security, protect patient privacy, and create an effective authentication system is crucial. The proposed formal model captures the complex interactions and behavior within the blockchain systems and emphasizing their robustness against various security threats. Through verification processes, model can ensure the correctness and security of authentication protocols. The provided results underscore the utility of Event B in detecting vulnerabilities and supporting the creation of dependable blockchain solutions for healthcare applications. This research adds to the existing knowledge by offering a systematic approach to safeguarding sensitive healthcare information through advanced authentication strategies.