If we install "modified games" on our iPhone or iPad, what risks are we exposing ourselves to?
Strongly recommend not to install such apps via any such (untrusted) medium

There's a likelihood that you may be exposing yourself to innumerable risks. These apps are distributed by gaming the Apple Developer Enterprise license.

They are distributed without going through the standard Apple's App Store Review Process. So it's likely that may be breaking one or more review guidelines and posing risk to the security of device and data.

Apple continuously discovers and suspend enterprise licenses where they are gamed to distribute apps to general public without going through the App Store Review process. Enterprise license is created solely for the purpose of distributing apps within an enterprise, and not to general public.


Apple's Enterprise Developer Program Also Being Used to Distribute Hacked Apps





  The only I can think of is that it fakes a log in screen to your iTunes account and lead you to type in the user name and password (Trojan horse), so I will always cancel such log in popup and go to iTunes and log in there myself.


If you are concerned about this particular risk, i.e. an app presenting a fake iTunes login popup and stealing password, there's an easy way to trust it's authenticity.

Just press the Home button (or on devices without Home button, navigate back to Home screen). If the popup is presented by the app (fake), it will be sent to the background along with the app. If the popup is presented by iOS (genuine), pressing Home button won't let you dismiss it. You will be able to dismiss it either by entering password or the pressing the cancel button.