Use the DISTINCT
keyword in a subquery to remove duplicates before combining the results: SQL Fiddle
SELECT
ProjectID
,STRING_AGG(value, ',') WITHIN GROUP (ORDER BY value) AS
NewField
from (
select distinct ProjectId, newId.value
FROM [dbo].[Data] WITH(NOLOCK)
CROSS APPLY STRING_SPLIT([bID],';') AS newID
WHERE newID.value IN ( 'O95833' , 'Q96NY7-2' )
) x
GROUP BY ProjectID
ORDER BY ProjectID