The Gemara (Bechoros 47a) states that if a non-Jew fathers a child with a Jew, the paternal relationship is not recognized from the perspective of the halacha. The child is viewed, in a manner of speaking, as if he were a product of parthenogenesis, as he has a legal mother but no legal father. That being the case, we have an extremely peculiar application: If a non-Levite Jew fathers a child with a daughter of a Levite, the child is given his father's affiliation, that of a non-Levite. If, on the other hand, a non-Jew fathered a child with a daughter of a Levi, the child would be a Levite.
This would not apply to the daughter of a kohen, because illicit intercourse would annul her kohanic status and therefore that of her child. If, however, the child was the product of in-vitro fertilization, then there are two possibilities.
1. If the donor was a non-Jew, then the donor is not recognized in halacha, leaving the child the mother's identity, her kedusha being intact, unlike the Gemara's example which involved illicit intercourse.
2. If the donor was a Jew, then there are two more possibilities. Some view the donor as the legal father, and therefore the child would not be a Kohen. Others do not accept the legal paternity of the donor, and therefore this would be a case of legal mother/no legal father, where we would apply the Gemara's rule of default matrilineal identity.