Hmm, it's not clear to me what "fields" 2 and 3 contain, so I'll assume field2 has the "4Q" and field3 has "12".

Just in case field1 is indexed, or it could be some day, let's avoid using functions on it (which is good technique anyway):

SELECT *

FROM dbo.tablename

WHERE Field1 >= '20' + field3 + CASE field2

WHEN '1Q' THEN '01'

WHEN '2Q' THEN '04'

WHEN '3Q' THEN '07'

WHEN '4Q' THEN '10' ELSE '01' END + '01' AND

Field1 < DATEADD(QUARTER, 1, '20' + field3 + CASE field2

WHEN '1Q' THEN '01'

WHEN '2Q' THEN '04'

WHEN '3Q' THEN '07'

WHEN '4Q' THEN '10' ELSE '01' END + '01')