Kaddish for a Secular Father

If someone did not observe Torah and mitzvot during their life and passed away, should their son recite Kaddish for them after their death?

The son should recite Kaddish for his father, even if the father did not observe Torah and mitzvot, and he should recite Kaddish for 11 months.

There is significant uncertainty among the poskim whether to define someone who does not observe Torah and mitzvot in our times as a mumar or as a tinok shenishba. Regarding a mumar, the Rema in Siman 376, paragraph 4, writes: "There is an opinion that if a mumar was killed by idolaters, his sons recite Kaddish for him (even though the Rema in Siman 340, paragraph 5, writes that they do not mourn for him, Kaddish is different, as Beit Hillel writes there. And it seems the reason is that they do not mourn for him because they do not grieve his death since he caused a great desecration of the Name in this world, but they recite Kaddish for him because he has atonement since he was killed by idolaters. And the Shach in SK 15 writes: "Only if he was killed, but if he died naturally, then not, and so I wrote above in Siman 340 that if he was killed, he has atonement, thus far the words of DM:" And the opinion is that if he died naturally, they do not recite Kaddish for him. However, the Gilyon Maharsha points out to the Rema from the response of the Radach (which is the source of the Rema's words) that Kaddish is recited for a mumar, and only if there is another mourner, the mourner for the mumar does not recite, because the recitation of Kaddish is an act of honoring the father, and the son of a mumar is not so obligated to honor him because he is wicked, but if there is no other mourner, the son of the mumar must recite Kaddish. And so ruled the Chatam Sofer in SHUT Siman 326. And so ruled the Ktav Sofer in Siman 109. Therefore, in places where it is customary for all mourners to recite Kaddish together, certainly one whose father did not observe Torah and mitzvot recites Kaddish with the other mourners. And even in places where it is customary to divide the Kaddish, the son whose father did not observe Torah and mitzvot has a Kaddish like everyone else, because it is accepted that one who received education not according to the way of Torah and reverence is considered a tinok shenishba.