Sensitive patient data is generated from a variety of sources and then transferred to a cloud for processing. Therefore, it is exposed to security and privacy and may lead to an increase in communication costs. Edge computing will ease computing pressure through distributed computational capabilities while improving security and privacy. In this paper, we propose a Federated PSN (FPSN) model where the model is moved directly to the edge to minimize computation and communication costs. PSN has been applied as a successful approach in categorizing and diagnosing patients based on similarities against some clinical and non-clinical features. Our proposed model distributes processing at each edge node, then fuses the constructed PSN matrices at the cloud premises, which significantly reduce the model's training and inference time and ensures quick model updates with the local client/nodes. In this paper, we propose: (i) an algorithm to evaluate patient's data similarity at the edge; and (ii) an algorithm to implement the federated similarity network fusion at the Cloud. We conducted a set of experiments to evaluate our FPSN model against other machine learning algorithms using a COVID-19 dataset. The results obtained prove that the FPSN model accuracy is higher than the distributed PSNs at various edges and higher than the accuracies of other classification models.