that lived in ukraine. who is their descents now? are they jewish or no?

Shalom, Thank you for your question. There is some historical debate as to the Kuzari nation (whose story is mentioned in the classic book The Kuzari by Rabbi Yehudah HaLevi). Many scholars believe that they were a nation who converted to Judaism in the past. As to their descendants today, to the best of my knowledge there is there is no particular group or lineage that associates itself with the Kuzari peoples. As to the Karaim, they are a religious group that was quite large 800 years ago. They still exist, albeit in very small numbers, in certain places in the world today (including Israel). Even though the Karaites originated as a breakoff group from the Jewish community, they are not recognized as Jews today – unless they return to accepted normative Judaism. Blessings.