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Instead of the cloud, the Internet of things (IoT) activities are offloaded into fog computing to boost the quality of services (QoSs) needed by many applications. However, the availability of continuous computing resources on fog computing servers is one of the restrictions for IoT applications since transmitting the large amount of data generated using IoT devices would create network traffic and cause an increase in computational overhead. Therefore, task scheduling is the main problem that needs to be solved efficiently. This study proposes an energy-aware model using an enhanced arithmetic optimization algorithm (AOA) method called AOAM, which addresses fog computing’s job scheduling problem to maximize users’ QoSs by maximizing the makespan measure. In the proposed AOAM, we enhanced the conventional AOA searchability using the marine predators algorithm (MPA) search operators to address the diversity of the used solutions and local optimum problems. The proposed AOAM is validated using several parameters, including various clients, data centers, hosts, virtual machines, tasks, and standard evaluation measures, including the energy and makespan. The obtained results are compared with other state-of-the-art methods; it showed that AOAM is promising and solved task scheduling effectively compared with the other comparative methods.