The main problem of your code has been solved. However, there are lots of other things that can be improved:

• Use the 3 argument version of open with lexical filehandles. Also, the open or die idiom is much more readable and common than your unless structure.
• Do not use the same name for various types of things (scalar and array variable in this case).
• If you can process the file line by line, do not slurp it all into memory.
• Use hashes to count numbers of occurrences.

Here is how I would approach your problem:

#!/usr/bin/perl
use strict;
use warnings;

print "Enter the file containing the sequence: ";
my $filename = <STDIN>;
chomp $filename;

open my $FH, '<', $filename or die "Cannot open $filename: $!";

my @chars = qw(A C D E F G H I K L M N P Q R S T V W Y);
my $length;
my $char_regex = join q(), @chars;
$char_regex = qr/[$char_regex]/;

my %occ;

while (my $line = <$FH>)
{
    for my $char (split //, $line)
    {
        next unless $char =~ $char_regex;
        $length++;
        $occ{$char}++;
    }
}

print "AMINO ACID \t OCCURRENCE \t FREQUENCY\n";

for my $char (@chars)
{
    $occ{$char} //= 0;
    print  "$char \t\t $occ{$char} \t\t ", $occ{$char} / $length, "\n"
+;
}
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BTW, the plus sign at 'S' just means your line is too long and has been wrapped. You can adjust your line length in your settings.