in case of unmarried parents "To legitimize a child, the father has to register a legimation of the child in Thailand with the local district office. then the registration allows the father to have the joint custody or sole custody over the child upon the agreement between the father and the mother of the child."
I guess you should get a paper from the district office stating that the father hasn't register such a legitimation.
It didn't happen to myself yet, but to other members of the French FB group. It seems that the family doctor has access to our files with the social security and can print out the two detailed certificates.