I include below what the Kollel wrote on this subject in Bechoros, which should provide you with the answer to your question.

Be well,

Mordecai Kornfeld

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Bechoros 47

1) A LEVI CHILD WHO IS "MEZUHAM"

OPINIONS: Rav Papa says that a firstborn son born to a Leviyah (the daughter of a Levi) who became pregnant from a Nochri is exempt from Pidyon ha'Ben. The Gemara explains that this ruling applies not only according to the opinion that "Ein Mezahamin Es ha'Vlad" ("we do not invalidate the child"), but even according to the opinion that "Mezahamin Es ha'Vlad" ("we invalidate the child"). The child is exempt from Pidyon ha'Ben because he is still considered a Levi.

What is the meaning of "Mezahamin Es ha'Vlad," and why is such a child -- born to a Jewish woman (who is a Leviyah) and a Nochri man -- still considered to be a Levi?

(a) RASHI (DH Ela Afilu) explains that according to the opinion that maintains "Mezahamin Es ha'Vlad," the child is a "Levi Pasul," a disqualified Levi, because his father is a Nochri. Nevertheless, he is a full-fledged Jew, because his mother is Jewish. According to the opinion that maintains "Ein Mezahamin Es ha'Vlad," the father has no relationship to the child at all and does not even disqualify the child from being a Levi.

(b) RASHI in Kidushin (68b, DH Leima) and TOSFOS in Yevamos (23a, DH Kasavar) write the opposite of what Rashi writes here. According to the opinion that maintains "Mezahamin Es ha'Vlad," we take the mother into consideration; since the mother is a Jew, the child is a Jew and is therefore declared to be a Mamzer (and a disqualified Levi). In contrast, the opinion that maintains "Ein Mezahamin Es ha'Vlad" maintains that the father does have some effect on the child, and the child is not a Jew. Since a Nochri cannot be called a Mamzer, the child is neither a Mamzer nor a Levi if he later becomes a Ger.

(c) TOSFOS here (DH v'Lo) makes an unusual compromise between the two approaches. When the Gemara says that the child is disqualified as a Levi because of "Mezahamin Es ha'Vlad," it is because we take into account the Nochri father, as Rashi explains in our Sugya. However, Tosfos also asserts that since we take the father into account, the child is considered to be a Nochri -- a Levi who is not a Jew! (The opinion that says "Ein Mezahamin Es ha'Vlad" will assert that the child is both a valid Jew and a valid Levi.)

How, though, can a Nochri be a Levi? While he is a Nochri, he certainly cannot serve in the capacity of a Levi. If he converts and becomes a Jew, he becomes a Yisrael, since he is not descended from the sons of Levi! (See SHA'AR HA'MELECH, Hilchos Isurei Bi'ah 15:3.)

A number of explanations are offered to explain the intention of Tosfos. (See MAHARIT ALGAZI (8:65a:2), who gives a very unusual explanation, which the BEIS YITZCHAK (Even ha'Ezer 1:29:8) uses in order to explain why Darius (Koresh II), the king of Persia, was considered a Nochri king (Rosh Hashanah 3b; see Insights there) even though he was the son of Esther, a Jewess.)

The NESIVOS HA'MISHPAT (in TESHUVOS HA'GA'ON MI'LISA #25) proposes that perhaps the rule that a Nochri who converts is considered to be newly born with no ancestry does not apply in its full sense to a child born to a Jewish woman and a Nochri. Once the child converts, he retroactively is considered to be the son of his Jewish mother. Therefore, if his mother is a Leviyah, then, he, too, is a Levi.

Alternatively, perhaps there is an error in the text of Tosfos here, and Tosfos is actually suggesting exactly the same explanation that he gives in Yevamos (23a, DH Kasavar). In the second line of Tosfos, the word "Mezahamin" should be "Ein Mezahamin," and in the third line of Tosfos, the words "k'd'Piresh b'Kuntrus" should be "v'Lo k'd'Piresh b'Kuntrus" (since, as Tosfos himself concludes, Rashi offers the exact opposite explanation). (M. Kornfeld)