Federated learning enables collaborative training across distributed sensor networks (DSNs) without requiring the sharing of raw sensing data. However, local updates can leak private information, and untrusted servers may return incorrect aggregation results. Existing verifiable secure aggregation schemes often incur high costs for resource-constrained devices. To address this, a verifiable and compressed FedAdam aggregation scheme (VCFedAdam) is proposesed. VCFedAdam performs masking, aggregation and verification operations within a low-dimensional sketch space, with the server recovering only the aggregated result for a fixed online set R, which consists of the users that successfully submit valid masked sketches in the current round and is fixed before aggregate recovery. Additionally, a commitment-bound verification (CBV) mechanism is designed to prevent the server from adaptively tampering with the aggregated results. At a compression ratio of $25\%$, experimental results show that VCFedAdam reduces computation overhead by $90.25\%$ and communication overhead by $75.38\%$ compared with traditional secure aggregation. On the CIFAR-10 and MNIST datasets, accuracy drops by only $0.64\%$ and $1.16\%$, respectively. Furthermore, security analysis confirms that VCFedAdam achieves both privacy protection and aggregation verifiability.