The problem is that you use the matching operator in scalar context instead of list context. In scalar context it would return the number of matches (0 or 1).

    my $pat = $line =~ m/^LOC_Os0[1-7]g[0-9]*.[0-9]\s/;
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should be

    my ($pat) = $line =~ m/^LOC_Os0[1-7]g[0-9]*.[0-9]\s/;
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I would write the script more like this in order to have error handling and avoid rewriting the whole file for each new entry.

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

open (FILE,  "<:utf8", "outputps_scan_chr1_.out");

my %seen = ();

open (MYFILE, ">:utf8", "data.txt");
open (WASTE, ">:utf8", "waste.txt");

while (defined(my $line = <FILE>))
{
    my $pat;
    next if ($line !~ m/^(LOC_Os0[1-7]g[0-9]*.[0-9])\s/);
    $pat = $1;
    if (!$seen{$pat}++)
    {
        print MYFILE $line;
    }
    else
    {
        print WASTE $line;
    }
}
close (MYFILE);
close (WASTE);
close (FILE);
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Update: I forgot to mention that I changed the pattern matching also.

First I want to know if there has been a match and then ignore the line, if there wasn't one.
Instead of matching a second time to get the pattern, I used a capture (...) in the pattern. Then I can retrieve the matched string in $1 and assign it to $pat.