Order by of records of a table in SQL Server
Test

WITH
cte1 AS ( SELECT 'US' country, 10 cnt
          UNION ALL
          SELECT 'UK', 2
          -- UNION ALL
          -- ... 
        ),
cte2 AS ( SELECT customer.*, 
                 country.name country, 
                 ROW_NUMBER() OVER (PARTITION BY country.name 
                                    ORDER BY customer.id) rn
          FROM customer
          JOIN country on customer.country_id = country.id 
        )
SELECT cte2.id CustomerID, cte2.name CustomerName, cte2.Country
FROM cte2
JOIN cte1 ON cte1.country = cte2.country
WHERE cte2.rn &lt;= cte1.cnt