It is, as is often the case, important to be exact in your use of terms.
When discussing visas, it is accurate to talk about Non B, Non O etc. In the case of applying for a Non O visa at a Thai embassy/consulate to visit your Thai child, there are no restrictions in terms of cohabitation or age. (Depending on the embassy/consulate, the birth certificate showing you as the father will usually be sufficient without legalisation.)
When talking about extensions of your permission to stay in Thailand, visas are irrelevant (except that you need to be on an entry from a non immigrant visa). You are seeking an extension to stay with your Thai child. In that case,
(i) you need to be living in the same household as your child; and
(ii) the child must either be under 20 years of age, or be seriously disabled to the point where they are unable to live independently.