Jamieson, Fausset and Brown on Matthew 1:12

12. And after they were brought to Babylon--after the migration of Babylon.

Jechonias begat Salathiel--So 1Ch 3:17. Nor does this contradict Jr 22:30, "Thus saith the Lord, Write ye this man (Coniah, or Jeconiah) childless"; for what follows explains in what sense this was meant--"for no man of his seed shall prosper, sitting upon the throne of David." He was to have seed, but no reigning child.

and Salathiel--or Shealtiel.

begat Zorobabel--So Ezr 3:2; Ne 12:1; Hag 1:1. But it would appear from 1Ch 3:19 that Zerubbabel was Salathiel's grandson, being the son of Pedaiah, whose name, for some reason unknown, is omitted.