Task offloading infers assigning of computational tasks from resource constrained IoT devices to more powerful infrastructure like edge servers, fog nodes or cloud systems. It enhances performance and optimized resource utilization. Secure Task offloading is very essential for protecting sensitive data, maintaining data integrity and preventing unauthorized access. Many models have been proposed for secure task offlloading however, less emphasis has given to the IoT device’s authentication. In the current work, a secure task offloading scheme is proposed by using a random nonce challenge based mechanism using AES encryption. The scheme ensures secure communication between IoT devices and fog nodes. Additionally, incorporation of the Highest Successful Task Completion (HSTC) ratio to offload the task to the eligible fog node is considered. For validating the approach, simulations have been conducted using Python. The performance of the proposed scheme has been improved across authentication time, energy consumption, cost, and detection accuracy as compared to earlier works published elsewhere. The scheme highlights the necessity of strong security mechanisms in edge computing environments while offering a secure approach for dynamic IoT networks.