If you just want a quick fix, try putting
$SIG{CHLD}='IGNORE';
in your main code. You may also need to put it in your forked children before you run the exec or system.

If you want a cleaner solution, setup your script to get the $pids.

You can use a different form rather than system or exec to get your pid. Also, there is the problem of getting the pid of the shell, which runs your command thru system or exec. You may need to use Proc::KillFam on the pid to get all it's children. See Best way to kill a child process

#!/usr/bin/perl
#When a program forks the fork returns the pid of the 
#child so the parent can use this to kill it at will.

my $pid = fork();
print "pid $pid created\n";

if ( $pid == 0 ) {
   # child process so do stuff here
   # usually have an exit to ensure child
   # does not escape this if clause
 exit;
}
else {
   # parent process, waits a while
   sleep 3;
   # kills child
   if( kill 9, $pid ){ print "pid $pid killed\n"};
}
# parent continues on here (as will child if not killed or exited)
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