Summary Cloud storage services require cost‐effective, scalable, and self‐managed secure data management functionality. Public cloud storage always enforces users to adopt the restricted generic security consideration provided by the cloud service provider. On the contrary, private cloud storage gives users the opportunity to configure a self‐managed and controlled authenticated data security model to control the accessing and sharing of data in a private cloud. However, this introduces several new challenges to data security. One critical issue is how to enable a secure, authenticated data storage model for data access with controlled data accessibility. In this paper, we propose an authenticated controlled data access and sharing scheme called ACDAS to address this issue. In our proposed scheme, we employ a biometric‐based authentication model for secure access to data storage and sharing. To provide flexible data sharing under the control of a data owner, we propose a variant of a proxy reencryption scheme where the cloud server uses a proxy reencryption key and the data owner generates a credential token during decryption to control the accessibility of the users. The security analysis shows that our proposed scheme is resistant to various attacks, including a stolen verifier attack, a replay attack, a password guessing attack, and a stolen mobile device attack. Further, our proposed scheme satisfies the considered security requirements of a data storage and sharing system. The experimental results demonstrate that ACDAS can achieve the security goals together with the practical efficiency of storage, computation, and communication compared with other related schemes.