Thanks for your reply.
I got stuck with finding out the proper settings.
My files are located in /www/example.com/public. This is set as document root in nginx server block.
In my pool of php-fpm I set a chroot path.
chroot = /www/example.com
That's why I have to set another path to document_root in my location block for php-files.
root /public;
With these settings all my php-files are delivered by php-fpm. Nothing to complain about. So, permissions and paths sem to be correct.
For security reasons I want to check, if the called file with php-extension really exists. For this purpose I want to use try_files. But when I put try_files $uri =404; in the php location block, I always get an 404 error for php-files.
I think nginx cant find the right path because of the chroot setting in php-fpm. Is the a way to get around this?