Limud Torah

We Paskin that a Ger could be Yoitze with children that he had while he was still a Goy. The Rambam and Tur say only if the kids also convert. The Bais Shmuel brings Shitos that argue and don't require the children to convert.
 
The Minchas Chinuch says that it's obvious that only if the children were with another Goy. Then, at that moment they were born, the children's pedigree follows their father. Even after the conversion, though they're not considered children anymore, since their pedigree follow the father, he's considered as fathering them and is Yoitze. But if he had the children with a Jewess where their pedigree follows the mother (that they are Jewish) and the father never had any connection with them from birth,  he's not Yoitze.