This study presents a novel approach for classifying electroencephalography (EEG) signals using federated learning and a client balancing technique, achieving an impressive accuracy of 99.14%. The proposed method addresses the challenges of data privacy and imbalance in client data by allowing selective participation in training based on data size while utilizing a ResNet50 deep learning architecture for optimal performance. The research aims to improve the diagnosis of neurological conditions while maintaining data security and efficiency in processing EEG data across various centers.