Disable Game Center in your app
You can enable or disable Game Center for your app at the version level. Once an app version is approved with Game Center enabled, Game Center can no longer be disabled within that version. Instead, you’ll need to disable Game Center when submitting an updated app version to the App Store.
From My Apps, select your app. The page opens with the App Store tab selected.
In the sidebar, click the app version under your desired platform, then navigate to the Game Center section.
Deselect the Game Center checkbox to disable Game Center for the version.