“And again the word of the Lord came unto Haggai in the four and twentieth day of the month, saying, Speak to Zerubbabel, governor of Judah, saying, I will shake the heavens and the earth; And I will overthrow the throne of kingdoms, and I will destroy the strength of the kingdoms of the heathen; and I will overthrow the chariots, and those that ride in them; and the horses and their riders shall come down, every one by the sword of his brother. In that day, saith the Lord of hosts, will I take thee, O Zerubbabel, my servant, the son of Shealtiel, saith the Lord, and will make thee as a signet: for I have chosen thee, saith the Lord of hosts.” Haggai 2:20-23.
Zerubbabel and his father Shealtiel (Salathiel) are the only two individuals found in both Matthew's and Luke's genealogy of Jesus between David and Joseph the husband of Mary. Apart from those two, every other name listed within that span is different in the two gospel accounts. See Human Ancestry of Jesus for more on that.
Zerubbabel is an important character. He was the governor of Judah for over twenty years, supervising the rebuilding of the temple in Jerusalem. The prophecies of Haggai and Zechariah were given to encourage him and Joshua the high priest in that important work. Haggai's messages to him personally have Messianic overtones, for their ultimate fulfillment would be realized in Zerubbabel's descendant, Jesus.
The question we are addressing here has to do with the differences in the biblical accounts of Zerubbabel's ancestry. 1 Chronicles 3:17-19; Matthew 1:12; and Luke 3:27 each give a different story.
The identity of Zerubbabel's father seems to clear. Ezra, Haggai, Matthew, and Luke all agree that Shealtiel (Salathiel) was Zerubbabel's father. Only the Hebrew text of 1 Chronicles lists Pedaiah as his father. The Greek Septuagint of 1 Chronicles lists Shealtiel as his father.
Jehoiachin (Jeconiah), who reigned as king in Judah for only three months and ten days, was taken to Babylon in 597 BC with the prophet Ezekiel and 10,000 other captives. He had a number of children, but none of them would ever reign as king (Jeremiah 22:30).
Our question is, was Shealtiel the son of Jehoiachin or the son of Neri? A number of possible explanations have been proposed. Shealtiel might have been the actual son of Neri (Luke 3:27), but the son of Jehoiachin (Matthew 1:12) by adoption. Or, if Jehoiachin's natural sons had all died, Jehoiachin might have chosen Shealtiel, the son of Neri, as his legal heir and successor. One other possibility is that Shealtiel was Jehoiachin's grandson--that Jehoiachin's daughter married Neri, and that Shealtiel was their son. With any one of these explanations, both Matthew's and Luke's accounts would be correct according to Jewish custom. Matthew, showing Jesus as a legal heir to Judah's throne, and Luke, possibly showing Jesus' actual blood line, are both correct.