as long as the father is the genetic father of the baby.
That’s interesting. Why would that be? I don’t see why the identity of the genetic father would make a difference (provided he wasn’t a Kohen, Levi or non-Jewish [and I’m not even certain about that last one]).
After all, even if she wasn’t married at all and had a firstborn boy, he would still need a pidyon. So, I fail to see why whether or not the child is the genetically related to the father makes a difference*.
The Wolf
* and just to head off the argument regarding possible mamzeirus — R. Moshe paskened that a child born to a married woman and a sperm donor is not a mamzer. And even if you don’t agree with R. Moshe and hold the child is a mamzer, he would *still* need a pidyon if he is the firstborn to his mother — just like he would still need a bris.