How do I stop the constant pop up on my iPad for APPLE ID VERIFICATION

This will pop all the time and is very annoying. It's says APPLE ID VERIFICATION PLEASE ENTER YOUR PASSWORD FOR(my email address) IN SETTINGS and then it gives you a choice of NOT NOW or SETTINGS. It doesn't matter how may times go to settings and enter your password it doesn't stop. I have called Apple 3 times and have even been to an Apple Store where they had a genius guy try to figure it out. Their ideals and solutions did not fix it.This is when I owned an iPad Air. I just decided to get rid of it because I couldn't get it to stop. I went and bought the new iPad Pro 9.7 and it's doing it again.I called Apple again and I have tried all the ideas and they had which included rebooting, resetting my iPad with erase all content and data and starting with a new iPad 8 times. They assured me this would fix the problem. Well, it hasn't. I had. I have google this question and I found that this same issue is happening to many people on their iPads and iPhones. I have tried everyone's suggestions which include things already tried as well as signing out of iCloud and then signing back in. Nothing helps. It still keeps popping up. It was also suggested that a app was stuck on trying to download and was causing the problem. I've checked and checked. Nope. Nothing stuck or not finished downloading. I think this is something in apples software. It has to be. If anyone has any answers please help.