how to find an application that was downloaded under a different apple id

There is another way given that your actual question is how to "find an application". The way I know of is to turn off automatic app updating. Start manually updating your apps, going down the list one by one. You will reach one (or more) that asks for a different acount. Delete that app. If you still wish to use it, download it with your own account.

How to manually update apps from the App Store - Apple Support

You will have to log in to the device using the Apple ID through which the App was downloaded from the App Store. There is no other way.