The recent developments in electronic and communication technologies have brought notable revolution in the e-healthcare industry for efficient transmission of the patient's data. One of the emergent applications of telehealth monitoring is the Internet of medical things (IoMTs). They are used to transfer and monitor medical information in patient-centred systems. Patient's data is very critical, so its secure transmission is of paramount requirement in smart healthcare applications. The current era has witnessed the large-scale usage of cryptographic and biometric systems, and machine learning (ML) approaches for authentication and anomaly detection, respectively, for securing medical systems. In IoMTs, sensor devices have limited power and battery, so to provide a balance between security and resource-efficiency is also an important aspect to consider during deploying IoMT. Therefore, this research aims to present an innovate framework to protect medical information from external threats with the consumption of less possible resources of low-powered medical devices. In this study, the ML-based biometric security framework is proposed in which features are extracted from Electrocardiogram (ECG) signals for the training phase. However, in the testing phase, the user authentication will be verified by utilizing generated unique biometric EIs from the ECG and acquired coefficients from polynomial approximation. The proposed framework has got the scientific as well as economic significance; thus, it could be used for real-time healthcare applications.