So i finally got this running (but i dont understand why) by just changing the folder structure.
Plesk Version 18.0.60
.Net Toolkit 2.1.12-2046
I copied this from the .net sample application you can create with plesk
api.at/webapp
api.at/index.html
Then i put the publish files from my application into the webapp folder.
In the .net settings:
Application URL
api.at
Application root
/api.at/webapp
Document root
/api.at/webapp/wwwroot
Application startup file
/api.at/webapp/application.dll