Welcome to Android Central! Which phone, and which email app? Have you checked the sync settings in the email app for your email accounts to make sure they're set to sync at a certain interval, rather than "None" or "Manual"? Also, is the phone's overall Auto-Sync toggle turned on?
I have a similar situation. I broke my original Galaxy S8 and just switched to a new one. I'm using the Samsung email app. I don't want to turn on sync but this box keeps popping up everytime I reopen the app. Also, I just updated to Oreo.