Is there a way to make iPhone forget the data belonging to one app? I recently downloaded an app (Rival Knights) which I already had on my iPad, but not on my phone. It gave me the option to write over my saved data and I declined. However now, I've changed my mind and want to start again.

I've tried deleting and re-installing the app, completely resetting my iPhone, deleting the app from my game centre, and making a new apple ID, however none of these have worked.

Is there any other way I can make my phone forget the app so I have a chance of starting again?
If you delete the app, all the data from that app gets deleted.

That is how the phone forgets that app.

If the app uses Game Center or another log in to retrieve game state from servers online, then you'll need to temporarily sign out of Game Center and possibly iCloud to remove those files from the phone as well.

I'd start by signing out of Game Center and delete/reinstall the game.

If that doesn't work, you can either check the specific game / contact that developer and/or sign out of iCloud documents or inspect that data store to see if that game has cloud files.

Once you have a clean start, you will know how to force a change to the cloud to reset the progress to be new.