You can attempt to put the ex boyfriend on child support, but he will oppose you petition, and the DNA test will show that he is not the father. Instead, you might consider putting the biological father on child support. It is irrelevant that he is/was married.
The fact that your ex-boyfriend signed the birth certificate while knowing that he was not the father does not make him responsible for supporting the child. (Actually, him signing the certificate was fraud considering that you both knew he is not the father.)
Yes, you can file a complaint (or open a DHR case) seeking to make him responsible for child support. However, he is within his rights to defend against it based on him not being the child's father. If he refutes paternity, no court will force him to pay support unless they first determine (through DNA testing) that he is biologically related to the child. Again, the fact that he supported his girlfriend's child does not make him responsible for supporting the child after the relationship with the mother ends. You cannot "make" him pay child support.
It sounds as if you were right to terminate your relationship with the child's father. However, you should not have allowed him to escape his responsibility for supporting your child. Since your child is entitled to the financial support of both of its parents, you really need to file a complaint for support (or open a DHR child support case) against the child's biological father. Him being married to someone else is irrelevant; he will still be made responsible for child support (as long as he either does not refute paternity, or is found by DNA testing to be the father).
The above answer is a general explanation of legal rights and procedures. It does not constitute legal advice. Nor does it establish an attorney-client relationship between the individual posting the question and the attorney providing the answer.
Ny colleagues have given sound information. Another thing to consider is that the only way to "make" your ex-boyfriend pay child support is to go to court, tell the court that he is the biological father, and ask for child support to be ordered. The ex-boyfriend will be given an opportunity to refute what you say. These days, DNA is used to prove or disprove paternity. If you are shown to be telling the court a false statement, then your credibility will suffer.
This communication does not establish an attorney-client relationship. This communication offers general information based on the limited facts set out in the question, and does not constitute the giving of legal advice. For specific legal advice, consult an attorney in your state who is knowledgeable in this area of law.