SQL Server 2017

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
create table tab (Name varchar(25), Domain varchar(25), Count int, datetime datetime);
INSERT INTO tab (Name, Domain, Count, datetime)
values
('John'    ,   'google'    , 5      , '2019-07-09 01:00:01'),
('John'    ,   'apple'     , 6      , '2019-07-09 01:02:01'),
('John'    ,   'apple'     , 8      , '2019-07-09 01:03:01'),
('John'    ,   'google'    , 10     , '2019-07-09 01:11:01'),
('John'    ,   'dos'       , 1      , '2019-07-09 01:11:01'),
('John'    ,   'dos'       , 3      , '2019-07-09 01:11:01');
6 rows affected

select name, domain, count,  CONVERT(varchar(10),datetime, 126) as datetime
from
(
select top 2 t.*
from tab t
where datetime >= CONVERT(datetime,'2019-07-08', 101) and
      datetime < CONVERT(datetime,'2019-07-10', 101)
order by row_number() over (partition by name, domain, cast(datetime as date) order by count desc) asc, count desc
) as t2
order by t2.datetime asc


name
domain
count
datetime


John
apple
8
2019-07-09

John
google
10
2019-07-09