MySQL 8.0

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CREATE TABLE `table` (ID INT, log_in VARCHAR(100) )
INSERT INTO `table` VALUES
(  1 , '[{"in_dt":"2020-01-01","in_by":"a"}]'),                   
(  2 , '[{"in_dt":"2020-01-01","in_by":"b"}]'),                   
(  3 , '[{"in_dt":"2020-01-02","in_by":"c"}]'),                   
(  4 , '[{"in_dt":"2020-01-05","in_by":"d"}]')

Records: 4  Duplicates: 0  Warnings: 0


SELECT *
  FROM `table` 
 WHERE DATE_FORMAT(JSON_EXTRACT(log_in,'$[0].in_dt'),'%Y-%m-%d')
           BETWEEN '2020-01-01' AND '2020-01-03'


ID
log_in


1
[{"in_dt":"2020-01-01","in_by":"a"}]

2
[{"in_dt":"2020-01-01","in_by":"b"}]

3
[{"in_dt":"2020-01-02","in_by":"c"}]

ID	log_in
1	[{"in_dt":"2020-01-01","in_by":"a"}]
2	[{"in_dt":"2020-01-01","in_by":"b"}]
3	[{"in_dt":"2020-01-02","in_by":"c"}]