The Rama quotes the Rashba: one is Yoitze P'ru Ur'vu if he has a child that's a Mamzer. Not only when they were from a permitted relation, like a Ger to a Mamzeres, but also if it came from an illicit relation, like a regular Jew with a Mamzeres or with an Ervah. This Halacha has support from a Yerushalmi. However, the Rif, Rambam and Rosh do not mention this Yerushalmi.
The Minchas Chinuch asks, why is he Yoitze through a forbidden relations. Isn't it a Mitzvah Habah B'Aveira (a Mitzvah that comes through a sin?) Even to those that say that you are Yoitze MiDoiraisah (from the Torah) still the Rabanan say you're not Yoitze?