Genealogy of Jesus Christ is mentioned in both the gospels of Matthew and Luke. However, there is one big problem: They differ each other.
Below is a tabulation of both accounts beginning from King David.
| Luke’s Account | Matthew’s Account |
|---|---|
 David |
David |
| Nathan | Solomon |
| Mattatha | Rehoboam |
| Menna | Abijah |
| Melea | Asa |
| Eliakim | Jehoshaphat |
| Jonam | Joram (aka Jehoram) |
| Joseph | Ahaziah |
| Judah | Joash |
| Simeon | Amaziah |
| Levi | Uzziah |
| Matthat | Jotham |
| Jorim | Ahaz |
| Eliezer | Hezekiah |
| Joshua | Manasseh |
| Er | Amon |
| Elmadam | Josiah |
| Cosam |
 (aka Eliakim) Jehoiakim |
| Addi | Jeconiah (aka Coniah, Jehoiachin) |
| Melchi | Shealtiel |
| Neri | Pedaiah? |
| Shealtiel | Zerubbabel |
| Zerubbabel | ? |
| Rhesa | ? |
| Joanan | Abihud |
| Joda | ? |
| Josech | Eliakim |
| Semein | ? |
| Mattathias | Azor |
| Maath | ? |
| Naggai | Zadok |
| Hesli | ? |
| Nahum | Achim |
| Amos | ? |
| Mattathias | Eliud |
| Joseph | ? |
| Jannai | Eleazar |
| Melchi | ? |
| Levi | Matthan |
| Matthat | ? |
| Eli | Jacob |
| Joseph | Joseph |
| Jesus |
Jesus |
The red color are from old testament which were missing from Matthew’s account. The crown icon represents that the descendant is a king and the no-child icon represents the cursed kings who will not have a seed to the throne of David.
Father of Zerubbabel?
Apart from Matthew mentioning the cursed royal line of Judah and relating it to Jesus, there is yet another problem with the genealogy where Zerubbabel is mentioned as a son of Shealtiel but he is actually the son of Pedaiah as per the old testament and Shealtiel is his brother. Hence, some had suggested Pedaiah may have died earlier and Zerubbabel is adopted (or) Pedaiah begat Zerubbabel raising a child for his brother’s name when Shealtiel died childless as per the law. Both are plausible but we cannot be sure.
Misconception
Jesus must come from a royal lineage: There is no prophecy that says the Messiah must come from a royal lineage. Neither Saul nor David were from a royal lineage. Messiah must only come from the lineage of David and sit on the throne of David.
Luke’s account is Mary’s: There is nothing to suggest Luke was referring to Mary’s lineage.
| Luke’s Account | Matthew’s Account |
|---|---|
| Ordinary Lineage through Nathan, who was not a king and nothing is known about him except being a son to king David | Royal Lineage through Solomon. This will make God’s word through the prophecy of Jeremiah regarding Jehoiakim and his son Jeconiah void |
| All names are mentioned but cannot be verified using Old Testament | Only some names are mentioned but counts it by 14 sets of generations which is wrong since Old Testament gives more names and more generations. |
Conclusion
Matthew had portrayed Jesus as someone special from birth having royal lineage and he got several things wrong in the process. This doesn’t mean Jesus isn’t special but the reasons mentioned to make him so special isn’t right because of incorrect information and making prophecies fail. This makes Luke’s genealogy of Jesus account more reliable.
The Matthew lineage is of Mary. There is a mistranslation in Matthew 1:16 when corrected has THAT JOSEPH as FATHER of Mary, not husband. That leaves Luke 3 giving husband Joseph’s lineage. And, indeed, this is all very important, all explained at: https://www.quora.com/Does-Matthew-1-16-have-a-mistranslation-and-if-corrected-is-Marys-lineage/answer/LeEric-Marvin
The brothers Shealtiel and Pedaiah both named a child Zerubbabel. Look at following lineage. 1st Chronicles 3:10-24 lists Pedaiah’s children and grand children, different then those listed elsewhere for Shealtiel.
The children of Pedaiah and Shealtiel are different except for Zerubbabel. And the children of both Zerubbabel’s are different.
As for the mention of childless. It was rhetorical. The end effect is as if they were childless. As the genealogies proved they did indeed have children.
Nobody pass that point every held title to the throne again, including Jesus Christ. While they all held the Davidic rights to the throne, circumstance prevent that from happening.