I'm unsure of how to ask this properly but I'll try and do my best - I'm by no means a Git aficionado, I know how to use the basic commands but not advanced terminology/functionality.
I have a private repository myrepo cloned from a private server git.mydomain.com. I'm familiar with the process of branching code on the same repository with git checkout -b mybranch - however I'd like to branch to GitHub rather than my private server, resulting in something like this:
Repo Branch Remote Location (Purpose)
------------------------------------------------------------
myrepo --> private --> git.mydomain.com (Incremental work)
|
+------> public --> github.com (Public releases)
Essentially I'd like to be able to git checkout public and git merge private.