If you're matching against some $string, \z matches the end of the string.

my $field = '*E2@x*PAP';
$field =~ /\*PAP\z/;
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You can also use $, which will match at the end of the string with or without a newline.

my $nl   = "newline\n";
my $nonl = "newline";
$nl   =~ /line$/;
$nonl =~ /line$/;
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Update: As Test::More:

use Test::More 'tests' => 3;

my $field = '*E2@x*PAP';
ok( $field =~ /\*PAP\z/, '\\z matches at end of string' );

my $nl   = "newline\n";
my $nonl = "newline";
ok( $nl   =~ /line$/, '$ matches newline at end' );
ok( $nonl =~ /line$/, '$ matches end of string without newline' );
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