1st of all, if your kid is born in usa/canada, he/she possesses usa/canada citizenship automatically, and canada (usa?) does not care if he/she owns china or Jamaica citizenship;

on the other hand, china gov'n disallows dual/multi nationality, as far as i undersand, they do not publicly say---kids in such case are not Chinese citizen, but

it is true that it is difficult to apply china passport (proof of china citizenship) for the kids.