Welcome to the Monastery, editholla!

You don't specify clearly where the letter at the end of your string is coming from, so in this example, I've just hardcoded it in.

I've made a few small changes, most notably using the three-argument form of open, and outputting the actual error message that was set if there is one ($!). I also changed from using a bareword file handle to a lexical one.

After each file found is opened, we loop through the file line-by-line, then using a regex capture, if anything is found fitting the criteria we put the found string into a hash as its key, thus eliminating duplicates.

use strict;
use warnings;

my $way = "test";
my (@rit, $rid);

opendir $rid, $way;

while ( my $entry = readdir $rid ) {
    next unless -f $way . '/' . $entry;
    next if $entry eq '.' or $entry eq '..';
    push @rit, $entry;
}

closedir $rid;

my %data;

for (@rit){

    my $cat = "$way/$_";

    open my $fh, '<', $cat or die "Can't open $cat: $!";

    while (my $line = <$fh>){
        chomp $line;
        if ($line =~ /(4\w{3}A)/){
            $data{$1}++;
        }
    }
}

for my $k (keys %data){
    print "$k\n";
}
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Output:

4060A
4099A
[download]