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use strict;
use warnings;
...

my @result = sort keys %{$hash->{"AAA"}};
print "@result\n";

KAY1 KAY2 KAY3 KEY1 KEY10 KEY123 KEY2 KEY3 KEY9

sub keycmp {
    
...

@result = sort keycmp keys %{$hash->{"AAA"}};
print "@result\n";

KAY1 KAY2 KAY3 KEY1 KEY2 KEY3 KEY9 KEY10 KEY123