I found information after WW2 ended, US forces had taken prisoner German army foreign volunteers of Kalmyk origin in Croatia. Then they were placed in "the camp for displaced persons" in Munchen, then applied for immigration into 17 countries but were rejected until they managed to move to America, where they managed to stay despite the Asian immigration exclusion. This happened thanks to the efforts of Tolstoy Foundation, who helped Kalmyk family of Remelevyh (Ремелевых) obtain citizenship with US Sumpreme Court recognizing Kalmyks as Europeans because of 350 years of living in European Russia.
I appreciate any help or advice on how non-professional historian can find this specific SCOTUS decision and/or anything else related to this story. I haven't had much luck exploring http://www.supremecourt.gov
I think you’re having trouble finding a Supreme Court case because there wasn’t one. There was a case before the Board of Immigration Appeals in 1951 that fits your description. One can find a discussion of this case, referred to by the first initial R—-, in this dissertation beginning on page 283:
The Immigration and Nationality Act of 1952 subsequently did away with the racial bar to immigration. Some accounts of Kalmyks in the US seem to conflate these events, even in scholarly works, saying that in 1951 Congress allowed Kalmyks to immigrate as Europeans.