With the fast growth of technologies like cloud computing, big data, the Internet of Things, artificial intelligence, and cyber-physical systems, the demand for data security and privacy in communication networks is growing by the day. Patient and doctor connect securely through the Internet utilizing the Internet of medical devices in cloud-healthcare infrastructure (CHI). In addition, the doctor offers to patients online treatment. Unfortunately, hackers are gaining access to data at an alarming pace. In 2019, 41.4 million times, healthcare systems were compromised by attackers. In this context, we provide a secure and lightweight authentication scheme (RAPCHI) for CHI employing Internet of medical Things (IoMT) during pandemic based on cryptographic primitives. The suggested framework is more secure than existing frameworks and is resistant to a wide range of security threats. The paper also explains the random oracle model (ROM) and uses two alternative approaches to validate the formal security analysis of RAPCHI. Further, the paper shows that RAPCHI is safe against man-in-the-middle and reply attacks using the simulation programme AVISPA. In addition, the paper compares RAPCHI to related frameworks and discovers that it is relatively light in terms of computation and communication. These findings demonstrate that the proposed paradigm is suitable for use in real-world scenarios.