I have a public PHP project in a GitHub repo, which contains just one branch (master).
I want to have a separate branch/fork that is private for me (I have paid for
1.) Is it possible to have a private branch on a public repo
From what I know, no.
2.) Can I fork my own public repo into my own private branch
No, you can't fork a full repo (1-n branches) into a single branch. Well actually you could, if you just fork the one branch of the full repo. Just add it as a remote or start from a clone.
You might also be interested in Sparse checkouts.
3.) If both the above the are possible which is the best way forward
n/a
4.) If neither are possible how should I proceed?
n/a