Owing to the breakthrough in mobile wireless communication technologies, almost everyone has been immersed into social networks, while fake news and misinformation are also being pushed into people’s minds with astonishing speed and breadth. The rising disparity between limited computing resources and the exploding news size necessitates innovative solutions to handle the challenge posed by booming data volume and make it more likely to differentiate fake news. In response to the aforementioned dilemma, the social-aware computation offloading system is analyzed, where the digital twin (DT) paradigm is used to simulate tasks offloading and assess the associated costs. Next, to obtain the best offloading choice, we fully consider the social relationship constraints and further propose an online task execution method that includes two stages of cluster selection and computing offloading, named TOFDS. Specifically, it exploits the technologies from multiobjective optimization and deep reinforcement learning (DRL) and realizes the joint optimization of resource utilization, load balancing, service latency, and energy consumption. Eventually, the comparative experiments demonstrate that TOFDS performs well when dealing with fake news data and can adapt to changes in dataset size and service clusters.