Quantum analysis is an emerging branch of study, which leverages the unique properties of quantum computing to address problems challenging for classical computation. It plays a crucial role in the field of quantum cryptography. Since Kuwakado and Morii distinguished a 3-round Feistel structure using Simon’s algorithm in 2010, the security of Feistel structures has garnered increasing attention. At CRYPTO 2022, Canale et al. provided an automated method for the key-recovery attack. Then, at ToSC 2024, Xiang et al. showed the links between quantum distinguishers and truncated differentials. In this paper, we simplify their theorem for practical search and propose a more convenient search framework for periodic distinguishers of GFS. Based on our framework, we successfully verify and optimize existing periodic distinguishers and make an application for multiple ciphers, achieving good results. In particular, this paper proposes the first 9-round periodic distinguisher for GFS-4F, improving on the previous work by one round. We also provide another 5-round periodic distinguisher for GFS-2F and the first 8-round periodic distinguisher for TWINE. Furthermore, we apply the search framework to multiple structures and ciphers, demonstrating the effectiveness of the algorithm.