Mails don't sycronize outside of my WLAN

Use the actual Version, have this problem since years.
But the settings look ok, so please help me out.

Lacking any specifics it’s hard to provide insights.

Please provide the vendor and android version of your device, K9 version number and your incoming and outgoing mail server settings.

Do other apps that need the internet work outside your WiFi rage? Sounds like an energy saving feature, though, that deactivates background sync on mobile.