Cyber–physical–social systems refer to new systems that involve a large number of Internet of Things (IoT) devices connected through an interconnected network. These systems gather data for various services such as transportation, energy, healthcare, etc. This data is then transmitted to the cloud layer for storage, processing, and access. To handle the significant workload offloaded from resource-constrained IoT devices without latency or bandwidth issues, a technology called fog computing has emerged as an intermediary layer between the cloud and IoT devices. The quality of service (QoS) provided by fog computing relies on efficient task scheduling to optimize energy consumption and maximum execution time. This task scheduling problem is known to be NP-hard and cannot be solved with high precision in a reasonable time using traditional techniques or existing metaheuristic-based task schedulers. Therefore, this study proposes a new multi-objective task scheduling approach based on a modified marine predators algorithm (MMPA) to simultaneously minimize energy consumption and make-span under the Pareto optimality theory. This variant is named the multi-objective MMPA (M2MPA). M2MPA enhances the performance of the MPA by incorporating the polynomial crossover operator to improve its exploration operator and the adaptive CF parameter to enhance its exploitation operator. The effectiveness of M2MPA is evaluated using eighteen tasks with different scales (small, large, and medium) and heterogeneous workloads assigned to two hundred fog devices with varying processing speeds. Finally, M2MPA is compared with six well-established techniques using various performance indicators, including carbon dioxide emission rate, flowtime, make-span, and energy consumption. The experimental findings demonstrate the substantial superiority of M2MPA over all competing algorithms across different performance indicators and the Wilcoxon rank-sum test. Quantitatively, M2MPA achieves an average make-span of 10.095, average energy consumption of 3.77E+06, average flowtime of 8.39E+03, and average carbon dioxide emission rate of 8.88E+06.