There are, in the church, two priesthoods, namely, the Melchizedek and Aaronic, including the Levitical Priesthood. Doctrines and Covenants 107:1-4
The Mormon faith believes there is a Levitical Priesthood still in existence today. That line came from Aaron.
According to the Bible, Moses' brother, Aaron, worked with Moses to help the people out of the Promised Land.
When God handed down the 10 Commandments, the Law and the rules for sacrifices in the tabernacle, He proclaimed Aaron as a priest.
“Have Aaron your brother brought to you from among the Israelites, along with his sons Nadab and Abihu, Eleazar and Ithamar, so they may serve me as priests." Exodus 28:1
Bring your fellow Levites from your ancestral tribe to join you and assist you when you and your sons minister before the tent of the covenant law. Numbers 18:2
Only Aaron and his sons and those from the tribe of Levi (one of Jacob's 12 sons) could be the priests serving in the tabernacle/temple. That is why they were called Levites.
When they tried to start the temple over again, during the time of Nehemiah, they searched the ancestral records for a priest.
These searched for their family records, but they could not find them and so were excluded from the priesthood as unclean. Nehemiah 7:64
When the records showed that someone was not an ancestor, they were disqualified from being a priest. The Biblenot only a Jew, but from the tribe of Levi
Someone must prove from their ancestoral records that they are first Jewish, then specifically a Levite. Even so, the role of the Levitical priest is non-existant because priests are not needed. Jesus took care of all the sacrifices, dying for all sins and for all mankind, so the position was downsized.
For Joseph truly testified, saying: A seer shall the Lord my God raise up, who shall be a choice seer unto the fruit of my loins. 2 Nephi 3:6
Joseph Smith also claimed to be from the line of Aaron, granting him the Aaronic Priesthood. Aaron was from the line of Levi, one of the 12 sons of Jacob. In this passage, it says that Joseph was prophesied to come from the line of Joseph (or the fruit of his loins). Joseph Smith could not be from two lines. This would make him part Jewish (Levi) and part Egyptian (Joseph's sons came from an Egyptian).