MySQL 8.0

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create table t (id int,status varchar(100),cnt int);

insert into t values
(1,'test1',1),
(1,'test1',1),
(1,'test2',1),
(1,'zer1',0),
(2,'exam1',1),
(2,'exam1',1),
(2,'zer2',0),(2,'exam2',1),(3,'mit1',1),(3,'mit2',1),(4,'term1',1);
select min(status),id,s from
(
select * from 
(
select id,status,sum(cnt) s from t 
 where cnt>0
 group by id,status
) as  t1 where t1.s in( select max(s) from 
                          (select status,id,sum(cnt) s from t
                           where cnt>0
                            group by
                          status,id) t2 where t1.id=t2.id
                           group by t2.id
                       )
                       ) as t3 group by id,s
                       
                     
                     
                       


min(status)
id
s


test1
1
2

exam1
2
2

mit1
3
1

term1
4
1