FOG-enabled cyber-physical systems (FOG-CPSs) open new security challenges as the local edge devices are easier to compromise than a traditional cloud server. Remote data integrity checking (RDIC) plays an important role in safeguarding against data corruption from a storage server. Certificateless cryptography (CLPKC)-based RDIC schemes do not suffer from the drawbacks of the public key infrastructure (PKI)-based RDIC protocols. Most of the CLPKC-based RDIC schemes proposed in the literature deal with personal data. However, in a FOG-CPS, it is also important to audit a data file shared by a group of edge devices. Most of the existing group shared data auditing schemes lack mechanisms to defend against a semi-trusted data auditor applicable for a FOG-CPS scenario. In order to address these issues, in this paper, we propose a novel CLPKC-based group shared data auditing protocol tailored to the specific security requirements of a FOG-CPS. Besides, we perform a detailed cryptanalysis of two existing CLPKC-based privacy-preserving group shared data auditing schemes. The formal security analysis of our proposed protocol establishes metadata and data integrity proof unforgeability and claimed zero-knowledge privacy and reliability properties through rigorous proofs in the random oracle model setting. Performance evaluations establish the efficiency of our proposed protocol.