The Samaritans are called Cutheans. They were brought into the area by Sennacherib after the Assyrians scattered the 10 Tribes of the Israelites. The Samaritans accepted the five books of the Torah and the book of Joshua as sacred, because the rebellious Israelites rejected the later biblical books that were written for the Davidian kings. The Samaritans never claimed to be Jews or Israelites.
That's the Rabbis version. The Samaritans don't accept it. The Samaritans claim (and secular history supports their claims) that the Assyrians only exiled the Israelite nobility, but that the commoners were left behind. They claim to be descended from that Israelite population that got left behind.
The Samaritans never claimed to be Jews or Israelites.
They don't claim to be Jews [because they believe they descend from the 9 northern tribes, excluding Judah, Benyamin and Shimon, and parts of Levi]. But they do claim to be Israelites.