Postgres 12

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CREATE TABLE users (
  user_id  serial PRIMARY KEY
, username text NOT NULL
);

INSERT INTO users VALUES
  (1, 'a')
, (2, 'b')
, (3, 'c');

set datestyle = 'MDY';  -- necessary to deal with non-ISO input properly

CREATE TABLE userdata (
  user_id int
, datetime timestamp
, input text
);

INSERT INTO userdata VALUES
  (1,'8/4/2019 0:55', 'Request')
, (1,'8/4/2019 0:56', 'Ticket')
, (1,'8/4/2019 2:08', 'Submit')
, (1,'8/4/2019 2:21', 'Submit')
, (2,'8/4/2019 13:10', 'Submit')
, (2, '8/20/2019 2:10', 'Ticket')
, (2, '8/20/2019 2:12', 'Ticket')
, (2, '8/20/2019 2:13', 'Request')
, (3, '8/20/2019 2:15', 'Request')
, (3, '8/19/2019 2:16', 'Ticket')
, (3, '6/12/2020 2:22', 'Submit')
, (3, '6/12/2020 2:26', 'Submit')
, (3, '6/12/2020 3:26', 'Ticket');

CREATE INDEX userdata_special_idx ON userdata
(user_id, (datetime::date) DESC NULLS LAST, datetime);
3 rows affected

13 rows affected

-- for many rows per user
SELECT u.user_id, d.*
FROM   users u
LEFT   JOIN LATERAL (
   SELECT d.datetime, d.input 
   FROM   userdata d
   WHERE  d.user_id = u.user_id         -- lateral reference
   ORDER  BY d.datetime::date DESC NULLS LAST, datetime
   LIMIT  1
   ) d ON true;


user_id
datetime
input


1
2019-08-04 00:55:00
Request

2
2019-08-20 02:10:00
Ticket

3
2020-06-12 02:22:00
Submit


-- for few rows per user
SELECT DISTINCT ON (user_id)
       user_id, datetime, input 
FROM   userdata
ORDER  BY user_id, datetime::date DESC NULLS LAST, datetime;


user_id
datetime
input


1
2019-08-04 00:55:00
Request

2
2019-08-20 02:10:00
Ticket

3
2020-06-12 02:22:00
Submit

user_id	datetime	input
1	2019-08-04 00:55:00	Request
2	2019-08-20 02:10:00	Ticket
3	2020-06-12 02:22:00	Submit