Apple - How to get rid of "You have new mail." in zsh

Whether zsh checks for new mail can be adjusted through the MAILCHECK parameter as described in zshparam(1). It specifies the interval in seconds between checks for new mail, a zero turns off the checks completely. So just put this into your zsh configuration file:

# don't check for new mail
MAILCHECK=0

It tells you that you have received some mails (for example, because of your configuration of cron).

The best way is to read this mail. Type mail: at least one mail should appear. You can read by typing its number ID. You can also directly delete it (or even multiple mails) by typing d 1-1344 (1-1344 being the range of your new mails' IDs). Leave mail with x.

So apparently some program (probably my MAMP) put an email in

/var/mail/

Deleting this message did the trick...