Please make sure, that only the user, which runs Apache or Nginx is set as the owner/group of those files/folders, has access to those files/folder. This will either be apache:apache or www-data:www-data, depending on your OS.
0770 is only the permissions, but not the owner, as requested.
When i try to chown the named directory im recieving the following error: chown: der Eigentümer von „/media/nextcloud/“ wird geändert: Die Operation ist n icht erlaubt
It certainly sounds like a fat/ntfs type of issue. If this drive is to be permanently associated with the server consider formatting it with ext3 ext4 (or another Linux offering)
Don’t forget to make sure the paths are still the same, otherwise you’ll also need to update your config.php file with the new path.
Also, if you don’t already, consider mounting the drive permanently in fstab under a path you specify. If it differs from currently you’ll need to update the config.php and database.
Oh right, sorry I glazed over a bit with the German
No point trying to format it with Windows, on the linux box you can locate the disk with sudo fdisk -l then use parted to start completely fresh with the disk. /dev/sda1 is normally the OS drive/partition. Please be careful…