Data-driven landscape across finance, government, and healthcare, the continuous generation of information demands robust solutions for secure storage, efficient dissemination, and fine-grained access control. Blockchain technology emerges as a significant tool, offering decentralized storage while upholding the tenets of data security and accessibility. However, on-chain and off-chain strategies are still confronted with issues such as untrusted off-chain data storage, absence of data ownership, limited access control policy for clients, and a deficiency in data privacy and auditability. To solve these challenges, we propose a permissioned blockchain-based privacy-preserving fine-grained access control on-chain and off-chain system, namely FACOS. We applied three fine-grained access control solutions and comprehensively analyzed them in different aspects, which provides an intuitive perspective for system designers and clients to choose the appropriate access control method for their systems. Compared to similar work that only stores encrypted data in centralized or non-fault-tolerant IPFS systems, we enhanced off-chain data storage security and robustness by utilizing a highly efficient and secure asynchronous Byzantine fault tolerance (BFT) protocol in the off-chain environment. As each of the clients needs to be verified and authorized before accessing the data, we involved the Trusted Execution Environment (TEE)-based solution to verify the credentials of clients. Additionally, our evaluation results demonstrated that our system (https://github.com/cliu717/AsynchronousStorage) offers better scalability and practicality than other state-of-the-art designs. We deployed our system on Alibaba Cloud and Tencent Cloud and conducted multiple evaluations. The results indicate that it takes about 2.79 seconds for a client to execute the protocol for uploading and about 0.96 seconds for downloading. Compared to other decentralized systems, our system exhibits efficient latency for both download and upload operations.