MariaDB 10.2

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CREATE TABLE T (Id INT, user_id INT, Name VARCHAR(1));
INSERT INTO T
SELECT 1, 1, 'A'
UNION ALL
SELECT 2, 1, 'B'
UNION ALL
SELECT 3, 1, 'C'
UNION ALL
SELECT 4, 2, 'D'
UNION ALL
SELECT 5, 2, 'E'
UNION ALL
SELECT 6, 2, 'F'
UNION ALL
SELECT 7, 1, 'G'
UNION ALL
SELECT 8, 1, 'H'
SELECT Id, user_id, Name
FROM  T T2
WHERE (SELECT  COUNT(*)
       FROM    T T3
       WHERE T2.user_id = T3.user_id
       AND T2.Id <= T3.Id) <= 2


Id
user_id
Name


5
2
E

6
2
F

7
1
G

8
1
H