How to prevent emails from popping up on home screen

Salutations Maynash, 

It sounds like you’re wanting to change the way you’re notified of new emails in the Mail app. The following articles go over how to change the settings:

Change notification settings on iPhone

Use notifications on your iPhone, iPad, and iPod touch

You’ll start in Settings > Notifications > Mail. 

From here you can change how or if you want to notified, whether you want those notifications to have sound, show on the Lock Screen, if you want them to have a preview, etc. 

Thanks.