open (FILE1, "<", "filein.txt") || die "$!";
open (FILE2, ">", "fileout.out") || die "$!";
my $counter;
while(<FILE1>){
  m/.+,.+,\d+,(\d+)_.+/;
  $counter->{$1}++ ;
  print FILE2 "$counter->{$1},$_";
}
close FILE1;
close FILE2; 


result would be :
1,WG0045068-DNA,A01,0,102186_A01_WTCCCT519791,...
2,WG0045068-DNA,B01,0,102186_B01_WTCCCT519793,...
3,WG0045068-DNA,C01,0,102186_C01_WTCCCT519805,...
1,WG0045068-DNA,A01,0,102187_A01_WTCCCT519791,...
1,WG0045068-DNA,B01,0,102188_B01_WTCCCT519793,...
2,WG0045068-DNA,C01,0,102187_C01_WTCCCT519805,...
3,WG0045068-DNA,A01,0,102187_A01_WTCCCT519791,...
2,WG0045068-DNA,B01,0,102188_B01_WTCCCT519793,...
4,WG0045068-DNA,C01,0,102186_C11_WTCCCT519805,...

not sorted, but sorting should not be a problem :)