@John *********
yep, being the biological father to a thai child born out of wedlock doesn't help unless you have gotten the family court or Amphur decree granting you legal parental rights
About all you could get without that is a 60 day visit thai family extension based on being the father of a thai child. That doesn't require any proof of funds, just the birth certificate (the child goes with you obviously) the house book listing, and copies of your passport etc plus 1900baht
Go to your immigration office and get the hand out listing the requirements to get the 60 day extension
That's about all there is available to you, other than that you'd have to exit/re-enter