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Underwater Acoustic Sensor Networks (UASNs) are pivotal for environmental monitoring, surveillance, and marine data collection. However, their open and largely unattended operational settings, constrained communication capabilities, limited energy resources, and susceptibility to insider attacks make it difficult to achieve safe, secure, and efficient collaborative learning. Federated learning (FL) offers a privacy-preserving method for decentralized model training but is inherently vulnerable to Byzantine threats and malicious participants. This paper proposes trust-aware FL for underwater sensor networks (TAFL-UWSN), a trust-aware FL framework designed to improve security, reliability, and energy efficiency in UASNs by incorporating trust evaluation directly into the FL process. The goal is to mitigate the impact of adversarial nodes while maintaining model performance in low-resource underwater environments. TAFL-UWSN integrates continuous trust scoring based on packet forwarding reliability, sensing consistency, and model deviation. Trust scores are used to weight or filter model updates both at the node level and the edge layer, where Autonomous Underwater Vehicles (AUVs) act as mobile aggregators. A trust-aware federated averaging algorithm is implemented, and extensive simulations are conducted in a custom Python-based environment, comparing TAFL-UWSN to standard FedAvg and Byzantine-resilient FL approaches under various attack conditions. TAFL-UWSN achieved a model accuracy exceeding 92% with up to 30% malicious nodes while maintaining a false positive rate below 5.5%. Communication overhead was reduced by 28%, and energy usage per node dropped by 33% compared to baseline methods. The TAFL-UWSN framework demonstrates that integrating trust into FL enables secure, efficient, and resilient underwater intelligence, validating its potential for broader application in distributed, resource-constrained environments.