Thank you for using Apple Support Communities!
I understand from your post that when trying to redownload a previously purchased app none of your purchases show up and you are prompted to purchase the app again. Are you using the same Apple ID in the iTunes and App Store that you used to originally purchase the app? If not, your purchases will not appear. In order for your purchases to appear you will need to sign out of the iTunes and App Store and then sign back in with the Apple ID used to purchase the app. Settings > iTunes and App Stores > tap Apple ID > Sign Out
If you are using the same Apple ID, you can also check your purchase history using iTunes on a computer.This article will provide you with the steps on how to view your purchase history from a computer using iTunes: See your purchase history in the App Store or iTunes Store - Apple Support
Let us know if you are able to see your purchases through iTunes or not and if you are using the same Apple ID. We can then provide you with additional assistance if necessary.
Best Regards.