Federated Learning (FL) for face recognition aggregates locally optimized models from individual clients to construct a generalized face recognition model. However, previous studies present two major challenges: insufficient incorporation of self-supervised learning and the necessity for clients to accommodate multiple subjects. To tackle these limitations, we propose FedFS (Federated Learning for personalized Face recognition via intra-subject Self-supervised learning framework), a novel federated learning architecture tailored to train personalized face recognition models without imposing subjects. Our proposed FedFS comprises two crucial components that leverage aggregated features of the local and global models to cooperate with representations of an off-the-shelf model. These components are (1) adaptive soft label construction, utilizing dot product operations to reformat labels within intra-instances, and (2) intra-subject self-supervised learning, employing cosine similarity operations to strengthen robust intra-subject representations. Additionally, we introduce a regularization loss to prevent overfitting and ensure the stability of the optimized model. To assess the effectiveness of FedFS, we conduct comprehensive experiments on the DigiFace-1M and VGGFace datasets, demonstrating superior performance compared to previous methods.