Biological father denies support to his daughter

I did not marry the father of my daughter (lets just call him Anton) since he was not yet annulled from his previous. My mother in law instead arranged a marriage between me and the brother of Anton for the sake that the child.will not be born out of wedlock but anton promised to be the one.to give financial support even though it will be written on my daughter's birth certificate that it is the brother who is the father of my child. Unfortunately Anton did not keep his promise ,.he did not provide financial support for my child. And 1 year after that he found a girlfriend. Now the girlfriend is claiming that Anton has no.responsibility since it was the brother that I married and the brother should be the one to provide support. Is the girlfriend in the right?

technically yes. since at the eye of the law, the father or your child is not anton but your husband based on the fact that he signed the BC. you will have to prove in court that in fact, anton is the father. however, keep in mind that doing this, it is the same as admitting that you commit a crime when you falsified the child's BC.
best thing for you to do right now is approach the parents of anton as they were the one who gave you this idea.

Even if Anton has recognized that my daughter is his?