Pidyon HaBen when the father is not Jewish - Igrot Moshe Yoreh Deah 1:195

In 1954, Rabbi Menachem Mendel Burstein of Kansas City asked Rav Moshe Feinstein about what to do in terms of pidyon haben for a child of a Jewish mother and a non-Jewish father [a pidyon is based on פטר רחם, the opening of the womb, and thus it is the mother that is the critical aprent in this regard. See Bechorot 46a for more on this]. Rabbi Burstein had recommended that the maternal grandfather perform the pidyon haben, and Rav Moshe was inclined to agree with this ruling, as the grandfather could step in via the rules of זכייה, especially since the non-Jewish father is halachically insignificant in this case. Additionally, since there was a concern that the child would not do a pidyon for himself once he grew older, it was deemed best to do the ceremony now with the grandfather in lieu of the father. Rav Moshe went so far as to side with those who felt that the grandfather could do the pidyon with a bracha, and that the child would not need to re-redeem himself once he came of age.

Rav Moshe noted that, if possible, it would be best if the money used in the pidyon could technically be given to the child for the express purpose of the pidyon, as this would allow them to fulfill the view of the Shach.

With regard to the recitation of the bracha of שהחינו, Rav Moshe felt that one could follow the view of the Chatam Sofer and recite the bracha in this case (against the position of the Tzlach).