You can use the following syntax.
NB the syntax endDate like '%10:00%'
works in MySQL 8 but is not accepted in MySQL 5 so I have used an explicit CAST(endDate AS CHAR(20))
which works in both.
create table t(
id int auto_increment primary key,
isOnPause tinyint,
endDate datetime,
otherCol varchar(10));
insert into t (isOnPause, endDate,otherCol) values
(1,'2022-03-29 10:00:00','other 1'),
(0,'2022-03-29 10:00:00','other 2'),
(1,'2022-03-29 11:00:00','other 3'),
(0,'2022-03-29 11:00:00','other 4');
select * from t
where isOnPause
and endDate like '%10:00%' ;
id | isOnPause | endDate | otherCol
-: | --------: | :------------------ | :-------
1 | 1 | 2022-03-29 10:00:00 | other 1
insert into t (isOnPause, endDate,otherCol)
select isOnPause,null,otherCol from t
where isOnPause
and CAST(endDate AS CHAR(20)) like '%10:00%' ;
select * from t;
id | isOnPause | endDate | otherCol
-: | --------: | :------------------ | :-------
1 | 1 | 2022-03-29 10:00:00 | other 1
2 | 0 | 2022-03-29 10:00:00 | other 2
3 | 1 | 2022-03-29 11:00:00 | other 3
4 | 0 | 2022-03-29 11:00:00 | other 4
5 | 1 | null | other 1
db<>fiddle here