@Sam *****
if you are the named Father of Thai child on the birth certificate you can obtain a Non O visa.
Following ASQ or your stay in Phuket go to the Thai Immigration office where you are living and ask for the list of requirements for the one year extension of stay based on your being the Father of the child Thai child.
You will need deposit of 400,000 in your name only in a Thai bank account to qualify for the one year extension of stay.
Has the fact that you are the father been recorded in the Amphur where you and Thai family live?
In a past posted reply by Tod Daniels....
"IF the child is born out of wedlock remember that 100% of the parental rights is the mother's and while the father can get a Non-O visa from a thai consulate in their country and a 60 day visit thai family extension with just their name on the birth certificate, unless they go thru family court or the child is old enough to pick out the father at the amphur and answer questions (usually between 6 and 8 y/o) they're not gonna get a year extension based on raising a half thai child"