How to fork a branch and not the repository?

In github (and in git's mental framework) you clone and fork repositories.

There's no way to fork a branch; that doesn't make sense. Just fork the project, and work off the branch you're interested in. You don't lose anything by doing so.

"Working off a branch" usually means you

  1. clone a repository (e.g. git clone http://repository), then
  2. check out the branch you're interested in (git checkout awesome-branchname),
  3. and create a new branch based of that (git checkout -b new-even-more-awesome-branch-name)

I usually go for the option described in How do I clone a single branch in Git?

git clone <url> --branch <branch> --single-branch [<folder>]

It is quick, clean, and if I want to create a new repo out of the branch it's also very easy to do.