Same as everyone else it would seem: if he finds out he's the biological father, he can sue to be recognize as the legal father, but he has to do so on short order (he can't keep it as an ace up his sleeve to extort the legal parents for years), and his request may not automatically granted by the courts since they may consider that the child's interests are better served by continuity.
I don't mean what the Finnish legal system would do.
I mean to ask the people on this thread what rights and obligations they think the bio father ought have in a situation like this.
It doesn't seem far off the mark, does it to you?
Yes, it does.
First, I don't understand what you mean by 'extorting the legal parents'. He can't 'extort' the bio mother. She can't somehow prove she isn't the bio mother. And I do not quite understand what it means to 'extort' the cuckolded husband. Extort him how?
I think the results in this case have come about because of a deeply flawed law. With respect to the cuckolded husband, I believe he has no moral obligation to parent a child that is not his. He did not consent to fatherhood and all the fantastic mental gymnastics offered by Toni and company cannot turn obvious non-consent into consent. Nor do I believe he is a monster for no longer having interest in parenting the child he didn't father. Feelings are beyond the scope of morality.
As for the bio father, it seems to me if any man is to be on the hook for paying parental dues, it is he. What he did was actually far closer to consent to be a father than what the cuckolded husband did.
So, we have the following situation:
A woman who cuckolded her husband.
A cuckolded husband who did not consent to being a father to the child.
A bio father who did consent to being a father, inasmuch as he impregnated a woman of his own free will.
If the cuckolded husband wanted visitation rights, his request should be considered and unless he is unfit somehow, should not be denied. He acted as a father during the time he was being deceived, and it would be wrong of the State to take away the commitment he made if he continues to want to make it, now with full consent of the situation. Of course, if he did not want to visit the child, the state cannot order him to visit the child.
The cuckolded husband should never be on the hook for maintenance/child support of any kind, including if he chooses to continue parental rights. Of course, he can pay if he wants to.
The bio father should be on the hook for maintenance/child support, because he is the bio father and he engaged in actions that indicated consent to be a bio father (unless he was underage and this woman raped him, or some similar circumstance). If he does not want to see the child, then of course the court cannot order him to see the child. If he does want to see the child, he should have visitation rights, again unless he is obviously unfit.
I do not see that the Finnish law would allow for that situation, and that is as close to a just outcome as I can build up.