Count with where clause
No, the syntax you have is not valid, it can be corrected by the use of a CASE expression.
(and I guess you have a GROUP BY a, b as you'd get an error otherwise).

select 
  a
  b,
  count(case when t1.u = 'UAE' then c else null end) as c1 
from t1 
group by a, b ;


Note that the ELSE NULL is redundant and can be removed as that is the default ELSE behaviour anyway:

select 
  a
  b,
  count(case when t1.u = 'UAE' then c end) as c1 
from t1 
group by a, b ;




There is a (SQL Standard) FILTER syntax that is close to your attempt but SQL Server has not yet implemented it:

select 
  a
  b,
  count(c) filter (where t1.u = 'UAE') as c1 
from t1 
group by a, b ;