He should be able to sue the wife for the cost of the lawyer.
These laws are perfect example why feminist mantra of "male privilege" is nonsense. No woman has ever been held liable for child support payments for her husband's children that are not hers.
First you automatically blame this woman specifically and all women generally for what is a state law passed by men. It just shows, again, your anti-women bent.
Second, women are "held liable for child support payments for her husband's children that are not hers" - but it is the second wives that pay the price in this case. I don't know about all states, but in some the second wife's income is considered in awarding child support for the ex-wife's children, but the second wife's children (expenses to raise them) are not. This results in the second wife having to subsidize the first wife's childrearing expense to the detriment of her own children.
I don't agree that the man in the OP should have to pay child support for a child that isn't his, but before you start any more of your misogynistic rants, perhaps you should educate yourself to the fact that the antiquated divorce and child support system actually hurts BOTH men and women at alarming rates.
ETA, from the comments Section of one of the articles:
Given how welfare works in most state, I would guess that it was neither a judge nor a mother who filed for child support...it was the state of Iowa. If the mother files for welfare benefits for herself and the child, then the state will automatically seek payments from the "father." In this case, because of the law, the government employee won't care if they are married or not, they must simply follow the law.
