The Open Science Framework (OSF) is a web service that has been created by the Center for Open Science (COS). This service facillitates the storage, management, and sharing of research data.
The QOpenScienceFramework module should be all you need to get started with connecting your PyQt application to the Open Science Framework (https://osf.io). It offers functions to easily communicate with the Open Science Framework API, and also a set of PyQt widgets (which should work with both pyqt4 and 5) that are designed to display and interact with the information the API provides. They furthermore allow you to download files from, or upload files to the OSF.
These are some example screenshots of the widgets:
And here is a video made by Sebastiaan Mathôt showing it in action (integrated in OpenSesame):