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While deep learning models like Vision Transformer (ViT) have achieved significant advances, they typically require large datasets. With data privacy regulations, access to many original datasets is restricted, especially medical images. Federated learning (FL) addresses this challenge by enabling global model aggregation without data exchange. However, the heterogeneity of the data and the class imbalance that exist in local clients pose challenges for the generalization of the model. This study proposes a FL framework leveraging a dynamic adaptive focal loss (DAFL) and a client-aware aggregation strategy for local training. Specifically, we design a dynamic class imbalance coefficient that adjusts based on each client's sample distribution and class data distribution, ensuring minority classes receive sufficient attention and preventing sparse data from being ignored. To address client heterogeneity, a weighted aggregation strategy is adopted, which adapts to data size and characteristics to better capture inter-client variations. The classification results on three public datasets (ISIC, Ocular Disease and RSNA-ICH) show that the proposed framework outperforms DenseNet121, ResNet50, ViT-S/16, ViT-L/32, FedCLIP, Swin Transformer, CoAtNet, and MixNet in most cases, with accuracy improvements ranging from 0.98\% to 41.69\%. Ablation studies on the imbalanced ISIC dataset validate the effectiveness of the proposed loss function and aggregation strategy compared to traditional loss functions and other FL approaches. The codes can be found at: this https URL.