If you modified git's history and the change was already pushed, you will usually get a
! [rejected] my-branch -> my-branch (non-fast-forward)
error, when trying to push.

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You can force the push, with
git push --force origin my-branch

Careful:

• You might lose history.
• Unless your git is configured to push only the current branch, you must supply the remote branch name or you will force-push all your branches!
• Anyone else who has already pulled the changes will run into significant trouble.

Only do this to instantly fix a mistake, or when you know exactly what you're doing.