If Game Center prompts you to load a different game, it means the Game Center you’re currently logged into is linked to another save-game.
To stop these prompts, please sign out of the current Game Center account, and sign back in with the correct one. To do this, follow these steps:
Enter your Device Settings
Scroll down to Game Center
Sign out of the current account
Sign back in with your own Game Center account
Only one save-game can be connected to your Game Center account, and this connection is permanent. If your current game is not connected to any Game Center account, it will connect automatically to the next unaffiliated Game Center account you log in with.
Remember: if your game is not linked to a Game Center account, it will be impossible to retrieve on other devices if it gets lost.
If this procedure does not work, and your Game Center account seems to be connected to someone else’s game, please get back to us and we’ll do our best to help out.