Creating a Min date with Session Date also included in the table
When you post questions like this, it's really helpful if you post your sample data as inserts, so anyone can hop in and immediately query it.

CREATE TABLE #whatever
(
    id INT,
    employeeid INT,
    sessionloginlocal DATETIME
);

INSERT #whatever ( id, employeeid, sessionloginlocal )
SELECT *
FROM (
VALUES 
(1,   354, '2017-12-12 07:29:36'),   
(2,   354, '2017-12-11 16:58:21'),   
(3,   354, '2017-12-12 10:59:34'),   
(4,   354, '2017-12-11 18:32:59'),   
(5,   354, '2017-12-11 18:33:34'),   
(6,   354, '2017-12-11 17:16:58'),   
(7,   354, '2017-12-12 10:56:29'),   
(8,   354, '2017-12-11 19:37:54'),   
(9,   354, '2017-12-12 10:57:52')
) AS x (id, employeeid, sessionloginlocal)


This code uses a case expression and MIN as a windowing function to find the min login time per user. When they match, we display it as a date. When they don't we display NULL.

SELECT *,
       CASE WHEN w.sessionloginlocal = 
               MIN(w.sessionloginlocal) OVER ( PARTITION BY w.employeeid ) 
               THEN CONVERT(DATE, w.sessionloginlocal)
               ELSE NULL
       END AS min_sessionlocal
FROM   #whatever AS w;