Can my husband be held legally liable for a child I had my a married man if paternity has been established and child support ordered

The child can't have two fathers - what do you mean by your husband being "legally responsible?" Support?

The bio father of my child thinks my husband is legally liable by law for his daughter because we are married. Paternity testing has been done with the bio and court ordered childsupport. Will my husband be liable for the child in any way except free will. I think not.

Your thinking is correct. In most states the presumed father of the child during a marriage would be the husband. But if there was a court challenge and his rights were taken away in favor of the Bio dad then he no longer has the legal ties to the child.

Your husband is merely the step father ( no legal responsilibty what so ever)

The two threads need combined I answered on the other thread but it is the same basic answer here. Your husband is the step father. Step parents have no real rights or responsibilities.