The healthcare Internet-of-Things (IoT) offers many benefits including data transmission in real-time mode, the ability to monitor the physiological state of the patient in a different interval of time. Devices such as blood-pressure monitors, glucose meters, heart monitoring implants, Electroencephalography (EEG), Electrocardiogram (ECG), and Electromyography (EMG) wearable devices allow health providers to collect the patient health information locally and make a real-time decision based on the Patient Health Data (PHD). Hospitals have been adopting the IoT for many years and now they have healthcare IoT devices in patients’ rooms and their bodies. However, the medical agencies, hospitals, and companies do not consider the security risk of healthcare IoT devices connected to a Local Area Network (LAN) or Wide Area Network (WAN). The IoT devices can be easily hacked and may lead to several potentially life-threatening risks due to poor authentication and encryption practices. Existing machine learning algorithms and blockchain approach working in the cloud computing environment are unable to meet the Quality of Service (QoS) like reliability, authentication, identification, and security requirements of healthcare IoT devices. Most of the traditional machine learning algorithms and techniques for healthcare IoT lacks the real-world implementation for secure data transmission. Therefore, blockchain is introduced for secure and reliable transaction in healthcare IoT. Whereas Fog Computing (FC) is introduced to extend the services of the cloud at the edge of networks. Integration of FC with blockchain can overcome the issue of healthcare IoT device identification, authentication, and verification for scalable frequent data transmission in a decentralized environment. Hence, a novel solution for the abovementioned problem is proposed using FC and blockchain. It includes an FC-based three-tier architecture, an analytical model, a mathematical framework, and an Advanced Signature-Based Encryption (ASE) algorithm for healthcare IoT device identification, verification, and Patient Health Data (PHD) authentication. The aim is to extend secure data transmission for healthcare IoT and end-users availing the real-time services. The proposed model and algorithm will be able to provide services for transaction and transmission near the edge in a secure manner. By analyzing the generated results from the proposed novel ASE algorithm for throughput, packet error, reliability, and malicious node detection accuracy; it is observed that the ASE algorithm in the FC environment easily outperforms the cloud and the other existing state of the art techniques such as FogBus, Femto cloud, Blockchain Fog-based Architecture Network (BFAN), and BeeKeeper. The malicious node detection accuracy of the ASE algorithm in the FC environment is 91% and in the cloud is 83%. Whereas the reliability percentage of the ASE algorithm in FC is 95% and in the cloud is 87%. The proposed approach is tested on simulators iFogSim (Net-Beans) and SimBlock.