Adam Clarke on Matthew 19:1

Beyond Jordan - Or, by the side of Jordan. Matthew begins here to give an account of Christ's journey (the only one he mentions) to Jerusalem, a little before the passover, at which he was crucified. See Mar 10:1; Luk 9:51.

Jesus came from Galilee (which lay to the north of Judea) into the coasts of Judea; and from thence, in his way to Jerusalem, he went through Jericho, (Mat 20:17, Mat 20:29), which lay at the distance of sixty furlongs, or seven miles and a half from Jordan, to the western side of it. See Joseph. War, book iv. chap. 8. sect. 3. It seems, therefore, most probable, that the course of Christ's journey led him by the side of the river Jordan, not beyond it. That the Greek word περαν, especially with a genitive case as here, has sometimes this signification, see on Joh 6:22 (note); see also Bp. Pearce.