<p>With the rapid development of cloud storage, its wide application has brought convenience but also raised critical challenges, especially in data integrity verification. Existing integrity auditing schemes often fail to consider the need for different auditing frequencies for files of varying values. To tackle this problem, this paper first analyzes the security vulnerabilities in Huang et al.’s scheme that supports different auditing frequencies through demonstrating two specific attack methods. Then, we propose an enhanced certificateless integrity auditing scheme with different audit frequencies for different value files (CIA-FV). Our scheme guarantees that the cloud storage provider (CSP) cannot forge proofs to pass the audits conducted by the third party auditor (TPA). Users determine the value of files and, through a random scrambling mechanism, randomly shuffle the file indices before sending them to the TPA. This ensures that the TPA is unable to extract data content or discern the value of files from the proofs. A detailed security proof is provided, and performance comparison results show that CIA-FV outperforms other existing schemes.</p>