MySQL 8.0

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SELECT VERSION();

VERSION()

8.0.12

SET @`json` := '["A", [{"B": "1"}], {"C": "AB"}, {"D": "BC"}]',
    @`value` := 'AB';
SELECT JSON_SEARCH(@`json`, 'one', 'AB');

JSON_SEARCH(@`json`, 'one', 'AB')

"$[2].C"

SELECT JSON_SEARCH('["A", [{"B": "1"}], {"C": "AB"}, {"D": "BC"}]', 'one', 'AB');

JSON_SEARCH('["A", [{"B": "1"}], {"C": "AB"}, {"D": "BC"}]', 'one', 'AB')

"$[2].C"

SELECT JSON_SEARCH('["A", [{"B": "1"}], {"C": "AB"}, {"D": "BC"}]', 'one', @`value`);

JSON_SEARCH('["A", [{"B": "1"}], {"C": "AB"}, {"D": "BC"}]', 'one', @`value`)

"$[2].C"

SELECT JSON_SEARCH(@`json`, 'one', 'AB');

JSON_SEARCH(@`json`, 'one', 'AB')

"$[2].C"

SELECT JSON_SEARCH(@`json`, 'one', @`value`);

JSON_SEARCH(@`json`, 'one', @`value`)

"$[2].C"

SHOW WARNINGS;
SELECT JSON_SEARCH(JSON_UNQUOTE(@`json`), 'one', @`value`);

JSON_SEARCH(JSON_UNQUOTE(@`json`), 'one', @`value`)

"$[2].C"