As one of the effective ways of ocular disease recognition, early fundus screening can help patients avoid unrecoverable blindness. Although deep learning is powerful for image-based ocular disease recognition, the performance mainly benefits from a large number of labeled data. For ocular disease, data collection and annotation in a single site usually take a lot of time. If multi-site data are obtained, there are two main issues: 1) the data privacy is easy to be leaked; 2) the domain gap among sites will influence the recognition performance. Inspired by the above, first, a Gaussian randomized mechanism is adopted in local sites, which are then engaged in a global model to preserve the data privacy of local sites and models. Second, to bridge the domain gap among different sites, a two-step domain adaptation method is introduced, which consists of a domain confusion module and a multi-expert learning strategy. Based on the above, a privacy-preserving federated learning framework with domain adaptation is constructed. In the experimental part, a multi-disease early fundus screening dataset, including a detailed ablation study and four experimental settings, is used to show the stepwise performance, which verifies the efficiency of our proposed framework.