It's always better to learn new things.

But in this case good old derived table will work pretty well:

select CONVERT (varchar(9),T.EMPLOYEE_ID) AS emp_id

, CONVERT(datetime,(CONVERT(varchar(8), T.ADMISSION_DTE))) AS Adm_date

, T.ADMISSION_CDE

, T.ADMIT_TYPE_CDE

, CONVERT(datetime,(CONVERT(varchar(8), T.DISC_DTE))) AS Dis_date

, T.DISC_CDE

, T.DISC_TYPE_CDE

from CurrentTable T

INNER JOIN (SELECT EMPLOYEE_ID, MAX(DISC_DTE) latest_dte

FROM CurrentTable

GROUP BY EMPLOYEE_ID ) LT ON LT.EMPLOYEE_ID = T.EMPLOYEE_ID AND LT.latest_dte = T.DISC_DTE

WHERE [BranchID]='950' AND (DISC_DTE IS NULL OR (DISC_DTE > 20120630 AND DISC_DTE < 20130201))

order by emp_id , adm_date