The typical industrial Internet of Things (IIoT) network system relies on a real-time data upload for timely processing. However, the incidence of device heterogeneity, high network latency, or a malicious central server during transmission has a propensity for privacy leakage or loss of model accuracy. Federated learning comes in handy, as the edge server requires less time and enables local data processing to reduce the delay to the data upload. It allows neighboring edge nodes to share data while maintaining data privacy and confidentiality. However, this can be challenged by a network disruption making edge nodes or sensors go offline or experience an alteration in the learning process, thereby exposing the already transmitted model to a malicious server that eavesdrops on the channel, intercepts the model in transit, and gleans the information, evading the privacy of the model within the network. To mitigate this effect, this paper proposes asynchronous privacy-preservation federated learning for mobile edge networks in the IIoT ecosystem (APPFL-MEN) that incorporates the iteration model design update strategy (IMDUS) scheme, enabling the edge server to share more real-time model updates with online nodes and less data sharing with offline nodes, without exposing the privacy of the data to a malicious node or a hack. In addition, it adopts a double-weight modification strategy during communication between the edge node and the edge server or gateway for an enhanced model training process. Furthermore, it allows a convergence boosting process, resulting in a less error-prone, secured global model. The performance evaluation with numerical results shows good accuracy, efficiency, and lower bandwidth usage by APPFL-MEN while preserving model privacy compared to state-of-the-art methods.