To run fetchmail as a systemd user service, for an individual user:

(1) Configuration

Set up your .fetchmailrc so that "fetchmail --nodetach" actually
fetches your mail correctly.

(2) Tell systemd to run it as a service

Allow daemons to keep running after you log out (optional):
$ sudo loginctl enable-linger $USERNAME

Make the service available:
$ systemctl --user enable fetchmail.service

Actually turn it on:
$ systemctl --user start fetchmail.service

Monitor it, to check if it's okay:
$ systemctl --user status fetchmail.service

Monitor it harder:
$ journalctl --user -xeu fetchmail.service