iPhone asking for Apple ID for a former roommate

I suppose you restored your iPhone 6 from a backup of your older phone. If I understand the issue well enough, the phone keeps asking you for your friend password because you have an app that is his. If this app is on your computer in iTunes, there is a solution.

In the iTunes' list view of your Apps, right-click on an app, "Get info" (or just press cmd ⌘+I), and, depending on your OS version, either go to the Summary or the File tab. The Apple ID of the buyer, as well as his name, will appear, and you just have to go through your files (pressing cmd ⌘+P and cmd ⌘+N) until you find the culprit.

Unfortunately, iTunes cannot sort apps by buyer. However, you could sort Apps by "Date Added" in the list view to make the whole process much easier.

If it's an app and you wanna find it quickly just go to updates on your phone, click 'update all' then when the phone asks for the other ID you cancel it. The apps that will stay on the updating list after finishing the update process are the ones on the other ID. (I know it coz I have some apps that jumped onto my phone at some point and now I'm totally gonna try changing the ID on them. Thanks, Lax!)