I can not see any error on your original script, maybe the problem is on the called script "mycode.pl". You should try to make your script work without any paralelism first:

my @list = glob("*.fasta");
foreach my $fname (@list) {
  my ($base) = split /\./, $fname;
  system "perl mycode.pl $base >~/MyPerl/result_ans/$base.out"
}
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and later, once you have it working, add the Proc::Queue bits:

use Proc::Queue size=>5, qw(system_back);

my @list = glob("*.fasta");
foreach my $fname (@list) {
  my ($base) = split /\./, $fname;
  system_back "perl mycode.pl $base >~/MyPerl/result_ans/$base.out"
}
1 while wait != -1;
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You can also activate Proc::Queue trace mode to see what's going on.