Edge computing paradigm deploys infrastructures on users' edge side, enabling data to be stored in edge storage systems. Thus edge computing finds a balance between remote cloud storage with high latency and local storage with limited resources. However, the frequent update of edge data increases the probability of data corrupting. To ensure availability and integrity of edge data without affecting future use, this paper proposes a certificateLess edge recoverable data auditing (CL-ERDA) approach with corruption localization. First, the certificateless network coding signature in CL-ERDA is utilized to generate the homomorphic authenticator, addressing public key certificate management issues while avoiding insecure key escrow problems. Then, CL-ERDA designs a two-phase auditing method, where only file-level aggregation proofs are respond in first phase of external check and the second phase of self-check is launched only when damaged data is detected, reducing communication overhead of the auditing. Moreover, CL-ERDA combines hierarchical check method with batch localization method to achieve locating efficiently all the corrupted data at one time rather than locating only one corrupted data at once. Finally, security analysis shows that the proposed scheme resists various attacks and supports the unforgeability of authenticators. Experimental results demonstrate that CL-ERDA is efficient in auditing and corruption localization.