SELECT distinct date, pseudo FROM logstable
  WHERE (date BETWEEN STR_TO_DATE('01.02.2019 07:10:00', '%d.%m.%Y %H:%i:%s') 
  AND STR_TO_DATE('15.02.2019 08:30:00', '%d.%m.%Y %H:%i:%s'))
  AND date BETWEEN STR_TO_DATE('07:10:00', '%H:%i:%s') 
AND direct="OUT";

SELECT distinct date, pseudo FROM logstable
  WHERE time(date) BETWEEN STR_TO_DATE('07:10:00', '%H:%i:%s') 
  AND STR_TO_DATE('08:30:00', '%H:%i:%s')
AND direct="OUT";