The din states that the first born son to his MOTHER (not c sec) has to have a pidyon haben if the Father of the the boy is not a Cohen or Levi, or the baby boy’s mother is not a Bat Cohen or Bat Levi.
I am a bat cohen and I had a first child a son and did not have a pidyon haben.
My eldest son had a son first, but her father claimed he was a Levi and baby did not have a pidyon haben. Three years later, my daughter in law’s uncle came to visit from Eretz (her father’s brother) and in shul they wanted to give him an aliya for a Levi. He said he was not a Levi. I then checked with the cemetary in Israel, what was written on his Father’s metzaiva, if he was a Levi. He was not, and therefore the little 3 year old had to have a pidyon haben then. My second son had a girl first.
Once, many years ago in our shtiebel, a wonderful man arranged for boys (who were not frum, but learning in a Jewish school), to come for Pesach from Hungary, to different families. Many did not have a pidyon haben and we had a beautiful ceremony (after Pesach), with all the booys who needed one, with a different Cohen performing one pidyon haben as per halacha. It was a beautiful scene. The Av Beth Din of London was also a Cohen and he, too came to perform the mitzvah. We had 14 Pidyon Habens with 14 Cohanim, followed by a seudah mitzvah! Absolutely beautiful!
My brother in law and sister in law had a first born son and they had a pidyon. When my nephew married, he had a Pidyon for his first born. Another nephew also had a pidyon for his first born. The other nieces had girls first, except one, who had a pidyon. Now everyone in the family is waiting for my last son to I’YH marry, to see if he will have a pidyon I’YH. (My husband is a Yisrael).
We should all have many simachot with simcha!