At the level of object-orientation that you are using, inheritance is defined using the @ISA array. For details, see Inheritance in perltoot. I might rewrite one of your classes as

package BasicX::AAA1;

use BasicX;
our @ISA = qw(BasicX); 

sub new {
  my $class = shift;
  my $args  = shift;

  my $newclass = $class->SUPER::new(
                            {
                               DEBUG      => $args->{DEBUG},
                               SETTTING1  => $args->{SETTING1},
                            }
                         );

  return $newclass;
}

1;
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Note the use of the SUPER pseudoclass -- see Overridden Methods in the same document. If your parent class is incautious about its blessing, your object will be in the wrong class, but that would have already been true with your old code.