The Internet of Things (IoT) plays an important role in various healthcare applications. Radio Frequency IDentification (RFID) is widely used as a leading identification technology in a variety of IoT-health applications. In 2020, the number of cases of novel Corona Virus Disease 2019 ( n COVID-19) was increased rapidly throughout the world. Herein, IoT-Health enables the more convenient ways to access remotely and efficiently the medical services for the patients, also provides health monitoring by the doctors, physicians, and nurses over the Internet. However, security and privacy are considered key concerns in RFID-based IoT-health systems due to wireless communication over the channel. There could be huge risks of leakage of the patient's sensitive information, medical data, privacy of the patients, and so forth. To overcome these shortcomings, we have put forward a secure and reliable RFID authentication protocol using Digital Schnorr Cryptosystem for IoT-Health in COVID-19 patients care named S R 2 AP-DSC. Compared with the similar existing protocols, the security analysis followed by the performance evaluation of our proposed protocol demonstrates the minimal computation overheads and also provides resistance to various well-known security attacks. The AVISPA and Scyther simulation results confirm that the proposed protocol is safe under active and passive attacks. The overall analysis shows that the S R 2 AP-DSC is relatively superior to the other similar existing protocols.