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I want to find a specific file that doesn't start with a,k,G or 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.
find . -name '[^akGQ]?[^0-9]*'
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
!( ... )
Required, but never shown