#!/usr/bin/perl-w
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You need a space between the program name and any switches you need to pass to the program.    Better to just use the warnings pragma:

#!/usr/bin/perl
use warnings;
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open(my $outfile, ">", "Motif_Result.txt");

...

open(FIH, $patternseq);
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You should always verify that the file opened correctly:

open my $outfile, '>', 'Motif_Result.txt' or die "Cannot open 'Motif_R
+esult.txt' $!";

...

open FIH, '<', $patternseq or die "Cannot open '$patternseq' $!";
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my $in;

while ($in=<FIH>)
{
         chomp($in);
         my @pats=split " ",$in;
         my $residue=shift@pats;
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That could more simply be written as:

while ( <FIH> )
{
         my ( $residue, @pats ) = split;
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         foreach my $nnn (@pats)  # @pats = (AAAAA, TTTTT, GGGGG);
         {
         $patsmap{$nnn}=@residue;
         }
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You don't put any values into @residue so that is the same as saying:

         foreach my $nnn (@pats)  # @pats = (AAAAA, TTTTT, GGGGG);
         {
         $patsmap{$nnn} = 0;
         }
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Perhaps you meant to use $residue instead of @residue?

        print "Patterns\t"; print "@pats";             print "\n";
        my $length = @pats;
        print "Total Patterns are: $length"; print "\n";
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Instead of five separate prints you just need one:

        print "Patterns\t@pats\nTotal Patterns are: ", scalar @pats, "
+\n";
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                 my @l = split('', $str);
                 my $length=@l;
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That is usually written as:

                 my $length = length $str;
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exit;
     }
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You exit the program at the bottom of the loop so you only ever read one line from your 'pat.txt' file.