Schizophrenia is a severe mental health condition that disrupts personal, social, and professional life, impacting millions worldwide. Early and accurate diagnosis is essential for improving patients’ quality of life. While artificial intelligence (AI) holds significant promise in this area, conventional AI approaches typically rely on centralized data, which poses challenges related to privacy, scalability, and accessibility. Federated learning (FL) addresses these issues by enabling decentralized model training across institutions while preserving patient confidentiality. This study implements a horizontal federated learning model to enable collaboration between different healthcare institutions (clients) for schizophrenia diagnosis using resting-state functional MRI (rs-fMRI) data. To tackle the inherent class imbalance in schizophrenia data, where positive cases are typically under-represented, our approach integrates the Tversky loss function. Building on this, we propose a personalization scheme that allows each client to adapt their own Tversky loss parameters, enabling more tailored optimization and improved performance across heterogeneous data distributions. Combined with FL aggregation algorithms tailored for non-IID data, TVFed-P effectively addresses both quantity and feature skew, which are commonly observed in many medical datasets. We present a comprehensive comparative analysis of our proposed model, TVFed-P, against both locally trained and centralized models reported in the literature. Our best-performing variant surpasses all baseline approaches, demonstrating superior performance. These findings reinforce the promise of federated learning as a secure and effective strategy for early schizophrenia diagnosis.