Federated learning methods offer secured monitor services and privacy-preserving paradigms to end-users and organisations in the Internet of Things networks such as smart healthcare systems. Federated learning has been coined to safeguard sensitive data, and its global aggregation is often based on a centralised server. This design is vulnerable to malicious attacks and could be breached by privacy attacks such as inference and free-riding, leading to inefficient training models. Besides, uploaded analysing parameters by patients can reveal private information and the threat of direct manipulation by the central server. To address these issues, we present a three-fold Federated Edge Aggregator, the so-called Edge Intelligence, a federated learning-based privacy protection framework for safeguarding Smart Healthcare Systems at the edge against such privacy attacks. We employ an iteration-based Conventional Neural Network (CNN) model and artificial noise functions to balance privacy protection and model performance. A theoretical convergence bound of Edge Intelligence on the trained federated learning model's loss function is also introduced here. We evaluate and compare the proposed framework with the recently established methods using model performance and privacy budget on popular and recent datasets: MNIST, CIFAR10, STL10, and COVID19 chest x-ray. Finally, the proposed framework achieves 90% accuracy and a high privacy rate demonstrating better performance than the baseline technique.