Matthew 1:11-15
Mat 1:11 (KJB)
And Josias begat Jechonias and his brethren, about the time they were carried away to Babylon:
(1 Chr 3:15-16 KJV) And the sons of Josiah were, the firstborn Johanan, the second Jehoiakim, the third Zedekiah, the fourth Shallum. {16} And the sons of Jehoiakim: Jeconiah his son, Zedekiah his son. Here we have another skip of a generation. Jechonias was born to Jehoiakim which was the second son of Josiah, who fathered four sons. This would be about the time of 587 B.C.
Mat 1:12 (KJB)
And after they were brought to Babylon, Jechonias begat Salathiel; and Salathiel begat Zorobabel;
Now we are in the time of the Babylonian captivity. Here we have another skip of a generation. (1 Chr 3:17-19 KJV) And the sons of Jeconiah; Assir, Salathiel his son, {18} Malchiram also, and Pedaiah, and Shenazar, Jecamiah, Hoshama, and Nedabiah. {19} And the sons of Pedaiah were, Zerubbabel, and Shimei: and the sons of Zerubbabel; Meshullam, and Hananiah, and Shelomith their sister: Jechonias had fathered Salathiel and Pedaiah, and Salathiel and the son of Salathiel was Zerubbabel. (Luke 3:27 KJV) Which was the son of Joanna, which was the son of Rhesa, which was the son of Zorobabel, which was the son of Salathiel, which was the son of Neri, There seems to be a difference here. In Matthew 1:12, it states that Zerubbabel was the son of Salathiel and in 1 Chronicles 3:18, it states that he was the son of Pedaiah. However, there is no problem here and nothing wrong with the text. (Ezra 3:2 KJV) Then stood up Jeshua the son of Jozadak, and his brethren the priests, and Zerubbabel the son of Shealtiel, and his brethren, and builded the altar of the God of Israel, to offer burnt offerings thereon, as it is written in the law of Moses the man of God. In Ezra 3:2, we see the same situation that Pedaiah is omitted just like Matthew omits Joash and Amaziah. It was common for a grandson to be named as a son in the genealogies. There could also be a possibility that Pedaiah was his biological father and Shealtiel his legal father. Pedaiah may have died after having Zerubbabel and his brother took on the legal responsibility of raising him.
Mat 1:13 (KJB)
And Zorobabel begat Abiud; and Abiud begat Eliakim; and Eliakim begat Azor;
There is no mention of Abiud in the genealogies in Chronicles but the Jews had kept meticulous records, especially of the lineage of King David since the Messiah was to come through that line. Abiud begat Eliakim and nothing is known of this Eliakim. Then Eliakim had begat Azor. Nothing is known of Azor. Of these three nothing is known of them nor their posterity outside what we read in this verse.
Mat 1:14 (KJB)
And Azor begat Sadoc; and Sadoc begat Achim; and Achim begat Eliud;
During the time in Babylon, the Davidic line was threatened with extinction and that is why these men are listed being in the direct line of David. There is nothing known of them outside of this verse, only that they carried the Davidic line which would culminate in the Lord Jesus Christ.
Mat 1:15 (KJB)
And Eliud begat Eleazar; and Eleazar begat Matthan; and Matthan begat Jacob;
There is nothing known about the first three names except that they were in the Davidic line. The fourth name of Jacob is the only one that something is known about and it is found in the next verse.