Who were the ancestors of the Samaritans of Jesus' day?

The Samaritans claimed that they were Israelite descendants of the Northern Israelite tribes of Ephraim and Manasseh,

Ephraim and Manasseh Israelites of the northern ten-tribe kingdom, but after the conquest of Samaria by the Assyrians in 740 B. C. E., it included the foreigners brought in by the Assyrians. In Jesus' day, rather than having a racial or political connotation, the name usually referred to those who belonged to the religious sect that was located in the vicinity of ancient Shechem and Samaria.