Albert Barnes Commentary Ezra 4:3

"But Zerubbabel, and Jeshua, and the rest of the heads of fathers` [houses] of Israel, said unto them, Ye have nothing to do with us in building a house unto our God; but we ourselves together will build unto Jehovah, the God of Israel, as king Cyrus the king of Persia hath commanded us." — Ezra 4:3 (ASV)

You have nothing to do with us – Because the Samaritans had united idolatrous rites with the worship of Yahweh (2 Kings 17:29–41). To have allowed them a share in restoring the temple would have been destructive of all purity of religion.

As king Cyrus ... commanded us – The exact words of the edict gave the right of building exclusively to those who should “go up” from Babylonia to Judea (Ezra 1:3).