Just to confirm - was your child born before you completed 5 years of residence in the UK? The date in your PR blue booklet is irrelevant. Under EEA regulations, PR is obtained automatically after 5 years of exercising treaty rights. EEA3 application is just confirmation of the status.
If he was born after the 5 years (and before tou received the blue booklet), the child is British from birth. If he was born before the 5 years, you can register him as BC (assuming he was born in the UK).
I suggest you start by reading
Citizenship FAQs - Common Questions - Read before posting - Children.