Epilepsy is one of the most prevalent paroxystic neurological disorders. It is characterized by the occurrence of spontaneous seizures. About 1 out of 3 patients have drug-resistant epilepsy, thus their seizures cannot be controlled by medication. Automatic detection of epileptic seizures can substantially improve the patient's quality of life. To achieve a high-quality model, we have to collect data from various patients in a central server. However, sending the patient's raw data to this central server puts patient privacy at risk and consumes a significant amount of energy. To address these challenges, in this work, we have designed and evaluated a standard federated learning framework in the context of epileptic seizure detection using a deep learning-based approach, which operates across a cluster of machines. We evaluated the accuracy and performance of our proposed approach on the NVIDIA Jetson Nano Developer Kit based on the EPILEPSIAE database, which is one of the largest public epilepsy datasets for seizure detection. Our proposed framework achieved a sensitivity of 81.25%, a specificity of 82.00%, and a geometric mean of 81.62%. It can be implemented on embedded platforms that complete the entire training process in 1.86 hours using 344.34 mAh energy on a single battery charge. We also studied a personalized variant of the federated learning, where each machine is responsible for training a deep neural network (DNN) to learn the discriminative electrocardiography (ECG) features of the epileptic seizures of the specific person monitored based on its local data. In this context, the DNN benefitted from a well-trained model without sharing the patient's raw data with a server or a central cloud repository. We observe in our results that personalized federated learning provides an increase in all the performance metric, with a sensitivity of 90.24%, a specificity of 91.58%, and a geometric mean of 90.90%.