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.
According to the Rambam that needs the children to convert, if the children are still minors, the father cannot assume he's Yoitze and still need to have more children. Since the children, when they come of age, can protest their conversion that was done while they were a minor and retroactively become Goyim again, maybe he'll be left with no Jewish children.