SQL Server 2019

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CREATE TABLE tablename (
  Name VARCHAR(4),
  Citizenship VARCHAR(7)
);

INSERT INTO tablename
  (Name, Citizenship)
VALUES
  ('John', 'US'),
  ('John', 'England'),
  ('Jim', 'Germany'),
  ('Mark', 'US'),
  ('Mark', 'Belgium');
5 rows affected

select t.* from tablename t
where t.citizenship = 'US'
or not exists (select 1 from tablename where name = t.name and citizenship = 'US')


Name
Citizenship


John
US

Jim
Germany

Mark
US


select distinct name,
       first_value(citizenship) 
       over (partition by name order by case when citizenship = 'US' then 1 else 2 end) citizenship
from tablename


name
citizenship


Jim
Germany

John
US

Mark
US