Вы можете использовать следующий запрос для получения ожидаемого результата:
SELECT *
FROM [usa].[dbo].[tmpDate]
WHERE (year = 2018 AND quarter >= 2) OR
(year = 2019 AND quarter <= 3);
Демо с примерами данных:
DECLARE @TempData TABLE ([year] INT, [quarter] INT);
INSERT INTO @TempData ([year], [quarter]) VALUES
(2018, 1),
(2018, 2),
(2018, 3),
(2018, 4),
(2019, 1),
(2019, 2),
(2019, 3),
(2019, 4);
SELECT *
FROM @TempData
WHERE ([year] = 2018 AND [quarter] >= 2) OR
([year] = 2019 AND [quarter] <= 3);
Выход:
year quarter
---------------
2018 2
2018 3
2018 4
2019 1
2019 2
2019 3