We have an web application, which lets the user write code and store it in an internal git repository on our server. Now we wanted to allow the user to share his code with h
As per jasonrudolph comment, it is not currently possible to restrict API access to a specific repository.
Deploy keys are the closest thing that provides this type of functionality. (This won't help you from an API perspective, but a deploy key might meet your underlying need.) If your application were to generate an public/private SSH keypair, and the user were to add the public key as a deploy key in the repository, then you could use the private key to access just that one repository (without having access to the user's other repositories).