Select max for a tuple in table

A window function like ROW_NUMBER() should provide the best performance:

SELECT host, job, folder, file, mtime
FROM (
  SELECT *, ROW_NUMBER() OVER (PARTITION BY folder, job ORDER BY mtime DESC) rn
  FROM tablename
) 
WHERE rn = 1

See the demo.
Results:

| host | job | folder | file | mtime |
| ---- | --- | ------ | ---- | ----- |
| 2    | j1  | f1     | e9   | 3     |
| 3    | j2  | f2     | e6   | 5     |
| 2    | j3  | f3     | e8   | 7     |

You can filter with a subquery:

select t.*
from mytable t
where t.mtime = (
    select max(t1.mtime) from mytable t1 where t1.folder = t.folder and t1.job = t.job
)

For performance, consider an index on (folder, job, mtime).

You did not specify how you want to handle potential top ties (rows that relate to the same folder and job with the maximum mtime): this query does return them.