Just in case this may be helpful as a future reference, here are two non-substr ways to get the results you want:

use Modern::Perl;

my $string = 'ATATTTATATTAT';

my ( $subStr1, $theRest1 ) = unpack '(a3)(a*)', $string;
say $subStr1;
say $theRest1, "\n";

my ( $subStr2, $theRest2 ) = $string =~ /(.{3})(.+)/;
say $subStr2;
say $theRest2;
[download]

Output:

ATA
TTTATATTAT

ATA
TTTATATTAT
[download]

unpack expands the original string into two chunks: the first being three characters and the second is the rest of the string. The second method uses two captures within a regex, matching three characters and then the remaining characters.