Not free if you are not citizen or PR. You claimed asylum and your child is not in Canada so not eligible for free education. Chances are nil for approval since you came to Canada without your child. Once you are PR, you can sponsor child and then child is eligible for free education.
So for now, your child has to come on study permit and pay international fees. If even approved but you need school admission, pay tuition, show living expenses and find a Canadian guardian.
Did you claim asylum or are you a private/government sponsored refugee? If claimed asylum then plan to be separated from child for several years until PR.