MySQL 8.0

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CREATE TABLE actors (
  `id` INTEGER,
  `actor_id` VARCHAR(4),
  `correct_id` INTEGER
);

INSERT INTO actors
  (`id`, `actor_id`, `correct_id`)
VALUES
  ('1', 'fghj', '0'),
  ('2', 'fghj', '0'),
  ('3', 'fghj', '0'),
  ('4', 'zxcv', '0'),
  ('5', 'zxcv', '0');
SELECT actor_id,MIN(id)
FROM `actors` 
GROUP BY actor_id


actor_id
MIN(id)


fghj
1

zxcv
4


UPDATE 
actors a1 INNER JOIN (SELECT actor_id,MIN(id) minid
FROM `actors` 
GROUP BY actor_id) a2 USING (actor_id)
SET correct_id = minid
SELECT * FROM actors


id
actor_id
correct_id


1
fghj
1

2
fghj
1

3
fghj
1

4
zxcv
4

5
zxcv
4