<p>The Internet-of-Things (IoT) led to the creation of intellectual industrial systems called Industrial-Internet-of-Things (IIoT). These systems utilize smart device, sensor, camera, and fifth generation technology for automate data collection and evaluation, improving manufacturing efficacy and addressing scaling difficulties. The Internet-of-Things devices encompass in adequate computing, memory, battery capabilities. To solve these difficulties, mobile edge computing (MEC) is included into Industrial-Internet-of-Things systems for lessens the computation load on the devices. This paper proposes a novel model of Task Offloading and Resource Allocation for Industrial-Internet-of-Things utilizing Domain-Adaptive Message Passing Graph Neural Network in Mobile Edge Computing Federation System (TORA-IIoT-DAMPGNN-MECFS).MEC federation is improving resource usage and load balancing in Industrial IoT systems with real-world restrictions. Here, Task Offloading and Resource Allocation using Domain-Adaptive Message Passing Graph Neural Network (DAMPGNN) for improving the power usage and latency of mobile edge computing-assisted Industrial-IoT network. The performance metrics, like Energy Delay Cost, Power Consumption and Latency are examined. The performance of TORA-IIoT-DAMPGNN-MECFS method provides 16.20%, 26.81% and 30.18% lower energy delay cost and 23.52%, 16.81% and 20.15% less energy use compared to the existing approaches: Deep reinforcement learning-dependent task offloading with resource allotment for IIoT in mobile edge computing federation scheme(DRL-TORA-IIoT), Deep reinforcement learning for time-power tradeoff online offloading in mobile edge computing-based IIoT (DRL-TETO-IIoT) and Task co-offloading for D2D-aidedMEC in Industrial-Internet-of-Things (TO-MEC-IIoT) respectively.</p>