There are a number of such peoples depending on how far back you go. Some of the more obvious ones include: Jews, Romani, Armenians, Kurds, Dravidians, Kalmyks, Chechens, Tibetans, and Uiyghur. There are uncountable others.
Judaism was persecuted by the Soviet Union. Jews have been persecuted almost constantly.
christians
They were killed or banished. Puritans were not very nice.
Jews were targeted by Nazis as weakening Germany. Many were imprisoned and executed. Another ethnic group involved in Nazi genocide were the Romani (gypsies).
"Barbarian" is a general derogatory term for any person or group that is perceived to be uncivilized. It doesn't refer to any specific group of people from history.
Jews were not the only people who suffered. But, along with the Gypsies they were the only people who were persecuted for their heritage, rather than choices that they made.
christians
It was the Tutsis that were being persecuted, by the Hutus.
It was often people part of the IRA or UVF during the troubles
Judaism was persecuted by the Soviet Union. Jews have been persecuted almost constantly.
Stallingrad
The Sinti and the Roma were lumped together under the heading "Gypsies", and, like almost every other group that weren't pure Aryan, they were persecuted and murdered as "undesirables" by the Third Reich.
In 1290 Edward I expelled the Jews from England. No reason has been recorded.
People are sometimes persecuted for belonging to a certain ethnic group (jews are not only a religion but also an ethnic group; also negroes, other non-whites in many countries), other minorities or majorities (e.g., homosexuals, women, etc.). Basically, anybody who is "different" from what a group in power considers the norm.
During World War II the Nazis persecuted and killed millions of Jews, Polish, Slavic and Romani people, the mentally and physically disabled, the deaf and blind, homosexuals, and political adversaries like communists, socialists, and social democrats.
Quakers
Nobody hahaha