Kohanim are not allowed to marry a convert. However, if such a case happens (where there is a fully valid conversion), what is the status of the child? On one hand, they would be chalal, but would that offspring be able to inherit the Levite tribe of their father?
Various shiurim and tapes have explained that a chalal is treated a a Yisroel and not a Levite. For example Rabbi Kaganoff gives the example of the son of a kohen who had married a divorcee had to perform a Pidyon Haben on his first born child.
The shiurim that I have seen explain the reasoning behind this, but I do not have the explicit citations right now.
Rambam does say
Yet if a chalal went ahead and offered a korban, his offerings are accepted after the fact (Maimonides, Bi'at Mikdash 6:10).
However, this is different and normally he is not allowed to even join the Leviim to sing or perform the Avodah of Levi in the Bais Hamikdash.
@Avrohom Yizchok--I am a safek challal, and my son therefore is too (I married a Yisroel). Rav Sternbuch shlita paskened that we were not chiuv to give my firstborn son a pidyon haben.– user19283Jun 28, 2019 at 13:38
Thank you for adding this personal information. The sofek kohen element is therefore enough to negate the need for pidyon haben. Jun 30, 2019 at 10:36
@AvrohomYitzchok You need to put the @ user ID in order to send a message to someone. spr22 would not have been notified of your comment. Jun 30, 2019 at 14:39