Mail keeps popping up while doing other things..

I use the default mail app on my MacBook. When I am doing other work on my laptop the application continues to pop up in front of what I am doing, very annoying.

Most other posts I have seen of this issue are when others do not use Mail and it asks them to sign in. In my case I use mail as my default mail application, it does not ask me to sign in. There are also no new e-mails half the time this happens.

How do I stop this from happening?

Thanks!