MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLE mytable(
   product_id INTEGER  NOT NULL
  ,name       VARCHAR(6)
  ,status     INTEGER 
  ,user       VARCHAR(6)
  ,keyid      INTEGER 
);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (598,'prrr',0,'john',10);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (598,'prod',1,'jane',11);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (456,'abcd',2,'mac',12);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (598,'prdd',2,'kate',13);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (598,'rdpd',2,'jane',14);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (456,'prrr',3,'john',15);
INSERT INTO mytable(product_id,name,status,user,keyid) VALUES (456,'abbb',3,'kate',16);
select product_id, min(keyid)
from mytable t
where not exists (
	select 1 
	from mytable t1 
	where t1.product_id = t.product_id and t1.status <> t.status and t1.keyid > t.keyid
)
group by product_id


product_id
min(keyid)


598
13

456
15


select t.*
from mytable t
where t.keyid in (
	select min(keyid)
	from mytable t
	where not exists (
		select 1 
		from mytable t1 
		where t1.product_id = t.product_id and t1.status <> t.status and t1.keyid > t.keyid
	)
	group by product_id
)


product_id
name
status
user
keyid


598
prdd
2
kate
13

456
prrr
3
john
15