Federated semantic segmentation enables pixel-level classification in images through collaborative learning while maintaining data privacy. However, existing research commonly overlooks the fine-grained class relationships within the semantic space when addressing heterogeneous problems, particularly domain shift. This oversight results in ambiguities between class representation. To overcome this challenge, we propose a novel federated segmentation framework that strikes class consistency, termed FedSaaS. Specifically, we introduce class exemplars as a criterion for both local- and global-level class representations. On the server side, the uploaded class exemplars are leveraged to model class prototypes, which supervise global branch of clients, ensuring alignment with global-level representation. On the client side, we incorporate an adversarial mechanism to harmonize contributions of global and local branches, leading to consistent output. Moreover, multilevel contrastive losses are employed on both sides to enforce consistency between two-level representations in the same semantic space. Extensive experiments on several driving scene segmentation datasets demonstrate that our framework outperforms state-of-the-art methods, significantly improving average segmentation accuracy and effectively addressing the class-consistency representation problem.