I want to find a specific file that doesn't start with
Q and in which the third letter in the name is not a digit.
I have tried many links, but found nothing regarding to this composite problem.
Assuming you mean third character as opposed to third letter;
find . -name '[!akGQ]?[!0-9]*'
In ksh you will have the negation file globbing pattern
!( ... ). So you could write