Making an open source contribution
You cannot make a branch on a repository you do not have push access to.
Typically, making an open source contribution looks like:
Read their README and CONTRIBUTING documents, as well as any developer documentation.
Make a fork of the repository under your own user or organisation.
Set up the project as directed by the documentation.
Make a new branch in your fork, make the changes there.
Make a pull request from your new branch, following the documentation.
