The problem here is that you're getting your $exon variable confused with $gtf[2]. You're using $exon to hold the counter which you increment on matching lines, but then you clobber it by assigning $gtf[2] to it after that, but then you don't use it after that. Also, if you're going to use a counter, you don't need to use a regex to increment the digit part of the field. Also, there's no need for an elsif when there are only two possibilities (eq and ne).

  if ( $gtf[9] ne $previous ){
    $exon = 1;           # reset counter
  } else {
    $exon++;             # increment counter
  } 
  $gtf[2] = "exon$exon"; # put counter back in field
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