Federated learning (FL) is a distributed training technology that enhances data privacy in mobile edge networks by allowing data owners to collaborate without transmitting raw data to the edge server. However, data heterogeneity and adversarial attacks pose challenges to develop an unbiased and robust global model for edge deployment. To address this, we propose Federated hyBrid Adversarial training and self-adversarial disTillation (FedBAT), a new framework designed to improve both robustness and generalization of the global model. FedBAT seamlessly integrates hybrid adversarial training and self-adversarial distillation into the conventional FL framework from data augmentation and feature distillation perspectives. From a data augmentation perspective, we propose hybrid adversarial training to defend against adversarial attacks by balancing accuracy and robustness through a weighted combination of standard and adversarial training. From a feature distillation perspective, we introduce a novel augmentation-invariant adversarial distillation method that aligns local adversarial features of augmented images with their corresponding unbiased global clean features. This alignment can effectively mitigate bias from data heterogeneity while enhancing both the robustness and generalization of the global model. Extensive experimental results across multiple datasets demonstrate that FedBAT yields comparable or superior performance gains in improving robustness while maintaining accuracy compared to several baselines.