Federated deep learning provides a safe and effective approach for tasks with distributed data, including assisted diagnosis of schizophrenia using brain images. It is utilized to train deep learning models collaboratively with information from multiple sites while protecting subject privacy. However, image data of patients are rare at each single site, which may result in poor classification performance. The incorporation of abundant brain image data of healthy controls from public datasets may help model training while the sample-imbalance issue may still decrease model performance. Constructing a federated anomaly detection model with these data can alleviate the problem. Therefore, we propose our federated few-shot domain-adaptive anomaly detection (Fed-FAAD) model to assist in the screening of patients with schizophrenia, which can utilize abundant public data of healthy subjects and a few labeled data of patients as well as healthy controls to train a reliable anomaly detection model without privacy disclosure. We use fMRI data of healthy controls from the Human Connectome Project and six independent sites of patients with schizophrenia and demographically matched controls for validation. Results at the six sites show that the average area under the curves (AUCs) of the proposed method achieve up to 78.1% and 82.5% in the 10-shot and 20-shot tasks, respectively, which outperform local anomaly detection models with improvements of 9.7% and 7.4%, respectively. The proposed framework can be applied to privacy-protecting distributed screening of patients with schizophrenia.