I was a bit confused about the requirements, but I think this code does it.This code does something. I'm not sure if it does what you want.

#!/usr/bin/perl -w
use strict;

my @strings = ("CATINTHEHATWITHABAT",
               "WERWERWAT134wAt");
               
my $regex = '\wAT';

foreach my $string (@strings)
{
   while ( $string =~ m/($regex)/gi)
   {
       printf "%s found at pos %2d in %s\n",
               $1, pos($string)-length($1)+1, $string;
   }
}

__END__
Prints:
CAT found at pos  1 in CATINTHEHATWITHABAT
HAT found at pos  9 in CATINTHEHATWITHABAT
BAT found at pos 17 in CATINTHEHATWITHABAT
WAT found at pos  7 in WERWERWAT134wAt
wAt found at pos 13 in WERWERWAT134wAt
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An update:

#!/usr/bin/perl -w
use strict;

my @strings = ("CATINTHEHATWITHABAT",
               "WERWERWAT134wAtThatat",
               "WERWERWAT134wAtThattat");
               
my $regex = '\wAT';

foreach my $string (@strings)
{
   while ( $string =~ m/($regex)/gi)
   {
       printf "%s found at pos %2d-%-2d in %s\n",
               $1, pos($string)-length($1)+1, pos($string),
               $string;
   }
}

__END__
Prints:
CAT found at pos  1-3  in CATINTHEHATWITHABAT
HAT found at pos  9-11 in CATINTHEHATWITHABAT
BAT found at pos 17-19 in CATINTHEHATWITHABAT
WAT found at pos  7-9  in WERWERWAT134wAtThatat
wAt found at pos 13-15 in WERWERWAT134wAtThatat
hat found at pos 17-19 in WERWERWAT134wAtThatat
WAT found at pos  7-9  in WERWERWAT134wAtThattat
wAt found at pos 13-15 in WERWERWAT134wAtThattat
hat found at pos 17-19 in WERWERWAT134wAtThattat
tat found at pos 20-22 in WERWERWAT134wAtThattat

Note: ranges do not "overlap", see "...Thattat"
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