Use:

find ./quellochecerco 2>/dev/null

This hides not just the permission denied errors, of course, but all error messages.

If you really want to keep other possible errors, such as too many hops on a symlink, but not the permission denied ones, then you’d probably have to take a flying guess that you don’t have many files called ‘permission denied’ and try:

find . 2>&1 | grep -v 'permission denied' > files_and_folders