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

my @files;
while (<DATA>)
{
   chomp;
   push @files, $_;
}

@files =  sort by_first_third @files;

sub by_first_third
{
   my ($Afirst,$Athird) = (split '_|\.',$a)[0,2];
   my ($Bfirst,$Bthird) = (split '_|\.',$b)[0,2];
         $Afirst <=> $Bfirst
                  or
         $Athird <=> $Bthird
}

print join ("\n",@files), "\n\n";
print "first file: $files[0]", "\n";
print "last file : $files[-1]", "\n";

=prints

971305332_XXXXXX12345678765463565E_28062011102508.TXT 
971305332_AAAAAAAA12345678765463565E_28062011102508.TXT 
971305332_CCCC12345678765463565E_28062011102508.TXT 
971305332_CCCC12345678765463565E_28062020102508.TXT
981139804_ABCDEF12345678765463565E_28062016102508.TXT 
981139804_ABCDEF12345678765463565E_28062016112508.TXT 
981139804_ABCDEF12345678765463565E_28062016172508.TXT  
981139804_ABCDEF12345678765463565E_28062017102508.TXT 

first file: 971305332_XXXXXX12345678765463565E_28062011102508.TXT 
last file : 981139804_ABCDEF12345678765463565E_28062017102508.TXT  

=cut


__DATA__
981139804_ABCDEF12345678765463565E_28062016172508.TXT  
981139804_ABCDEF12345678765463565E_28062016112508.TXT 
981139804_ABCDEF12345678765463565E_28062016102508.TXT 
981139804_ABCDEF12345678765463565E_28062017102508.TXT 
971305332_XXXXXX12345678765463565E_28062011102508.TXT 
971305332_AAAAAAAA12345678765463565E_28062011102508.TXT 
971305332_CCCC12345678765463565E_28062011102508.TXT 
971305332_CCCC12345678765463565E_28062020102508.TXT