Deploying a mobile edge computing (MEC) server in the mobile blockchain-enabled Internet of things (IoT) system is a promising approach to improve the system performance, however, it imposes a significant challenge on the trust of the MEC server. To address this problem, we first propose an untrusted MEC proof of work (PoW) scheme in mobile blockchain networks where plenty of nonce hash computing demands can be offloaded to the MEC server. Then, we design a nonce ordering algorithm for this scheme to provide fairer computing resource allocation for all mobile IoT devices/users. Specifically, we formulate the user’s nonce selection strategy as a non-cooperative game, where utilities of the individual user are maximized in the untrusted MEC-aided mobile blockchain networks. We also prove the existence of Nash equilibrium and analyze that the cooperation behavior is unsuitable for blockchain-enabled IoT devices by using the repeated game. Finally, we design the blockchain’s difficulty adjustment mechanism to ensure stable block times during a long period of time. Compared with the weighted round-robin algorithm, our proposed nonce ordering algorithm can provide fairer computation resources and optimal nonce selection strategies for all mobile users. Network stability is gained through the proposed blockchain’s difficulty adjustment mechanism. The analysis and optimization results provide valuable design insights for practical mobile blockchain IoT systems.