Cloud storage has become a keystone for organizations to manage large volumes of data produced by sensors at the edge as well as information produced by deep and machine learning applications. Nevertheless, the latency produced by geographic distributed systems deployed on any of the edge, the fog, or the cloud, leads to delays that are observed by end-users in the form of high response times. In this paper, we present an efficient scheme for the management and storage of Internet of Thing (IoT) data in edge–fog–cloud environments. In our proposal, entities called data containers are coupled, in a logical manner, with nano/microservices deployed on any of the edge, the fog, or the cloud. The data containers implement a hierarchical cache file system including storage levels such as in-memory, file system, and cloud services for transparently managing the input/output data operations produced by nano/microservices (e.g., a sensor hub collecting data from sensors at the edge or machine learning applications processing data at the edge). Data containers are interconnected through a secure and efficient content delivery network, which transparently and automatically performs the continuous delivery of data through the edge–fog–cloud. A prototype of our proposed scheme was implemented and evaluated in a case study based on the management of electrocardiogram sensor data. The obtained results reveal the suitability and efficiency of the proposed scheme.