@Adam *****
as people have told you IF you have not gone thru family court and been granted legal parental rights, you as a foreign male who has a child with a thai woman out of wedlock have no parental rights and there for have no ability to get a year extension inside the country.
It doesn't matter if your name is on the birth certificate, it doesn't matter if your half thai child holds a passport from your country. The only thing that matters is whether you have been granted parental rights by either going thru the process in family court OR (if the child is old enough) by going to the local Amphur (city hall) and doing it there.
So the question I have to you IS
Did you go thru family court OR to the local Amphur to get parental rights granted ? If the answer to that question is no, then you can't get a yearly extension inside the country