In commercial fog computing, block-level client-side deduplication (BC-Dedu) can be used to save storage space and network bandwidth. However, the existing BC-Dedu schemes cannot support ownership management, which leads to the degradation of forward and backward secrecy of the outsourced data. Besides, BC-Dedu schemes are vulnerable to the side information leakage issue since the existence of data is revealed to the outside adversary. In this paper, we propose an anti-leakage BC-Dedu scheme that supports ownership management in fog computing. Specifically, we present a dual-level ownership list and key update mechanism to achieve ownership management in the proposed scheme. Besides, we construct a novel deduplication protocol to alleviate the side information leakage issue. Furthermore, a dynamic data storage strategy is proposed to reduce service costs and latency. Security and performance analyses demonstrate that the proposed scheme achieves the desired security requirements while saving resource efficiently.