The emergence of mobile edge computing (MEC) has facilitated the development of data caching technology, which enables application vendors to cache frequently used data on the edge servers close to the user, thereby providing low-latency data access services. However, in an unstable MEC environment, the multi-replica data cached by different edge servers is prone to corruption, making it crucial to verify the consistency of multi-replica data on different edge servers. Although the existing research realizes data integrity verification based on the cooperation of multiple edge servers, the integrity proof generated by multiple copies of data is the same, which has low verification efficiency and is vulnerable to attacks such as replay and replace. To address the above issues, based on homomorphic hash and sampling algorithms, this paper proposes an efficient and lightweight multi-replica integrity verification algorithm, which has significantly less storage cost and computational cost and can resist forgery and replay and replace attacks. Based on the verification algorithm, this paper further proposes a multi-replica edge data integrity collaborative audit scheme EDI-C based on the reputation model. EDI-C realizes the efficient collaborative audit of multiple edge servers in a distributed discrete environment through an incentive mechanism to avoid the trust problem of both sides caused by centralized audit. Also, it supports batch auditing of multiple copies of original data files at the same time through parallel processing and data block auditing technology, which not only significantly improves the verification efficiency but also realizes the accurate location and repair of corrupted data at the data block level. Finally, the security analyses and performance evaluation show the security and practicability of EDI-C. Compared with the representative schemes, the results show that EDI-C can ensure the integrity verification of cached data more efficiently in an MEC environment.