你需要分开比较 Date 价值与 Time 价值观。
您可以尝试此查询。
测试DLL

CREATE TABLE my_table (
    created_time  DATETIME
);

INSERT INTO my_table VALUES ('2018-04-01 14:00:00');
INSERT INTO my_table VALUES ('2018-04-01 14:50:00');
INSERT INTO my_table VALUES ('2018-04-04 10:00:00');
INSERT INTO my_table VALUES ('2018-04-01 15:00:00');

查询

select * from my_table 
where 
    (created_time between '2018-04-01' and '2018-04-30') 
AND 
    (CAST(created_time AS time) > CAST('14:30:00' AS time) AND CAST(created_time AS time) < CAST('16:30:00' AS time))

[结果]：

|         created_time |
|----------------------|
| 2018-04-01T14:50:00Z |
| 2018-04-01T15:00:00Z |

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