Clone means that origin url is exact url you cloned from. Push uses origin url.
You want to fork ๐ด the repo -> split your own code from original and make it run at its own thing (when you draw the commit tree, the bottom is the single line and then higher up they split into two or more, giving the fork teeth).
It can be done in github/other git repo hosting by hitting fork button and then cloning the resulting repo...
But you can also just change config of your existing repo.
You need to change upstream (imagine the forking lines being a stream - you gotta swim back to where original was) to point to original, and make your own repo url be a new origin remote.
This shows the commands to do those steps - https://gist.github.com/ElectricRCAircraftGuy/8ca9c04924ac11a50d48c2061d28b090
From step 2.