MySQL - Many to Many Join. Left Join already Present
As a rule of thumb conditions on the Outer table are usually placed in WHERE, but on the Inner table in ON:

SELECT  DISTINCT student.Student_ID as 'Student_ID',
                  case when class.class_id is null then 'No Class ATM' else class.class_id end as 'Class_ID',
                  case when Attendance.Attendance_Status is null then 'Not Present' else Attendance.Attendance_Status end as 'attendence_status'
          FROM Student
          LEFT JOIN Student_Has_Class ON(student_has_class.student_id = student.student_id)
          LEFT JOIN class ON class.class_id = student_has_class.class_id
            AND NOW() between class.class_start_timestamp and class.class_end_timestamp
          LEFT JOIN Subject ON(class.subject_id = subject.subject_id)
          LEFT JOIN Attendance on(Attendance.class_id = class.class_ID
                                  AND Attendance.student_id = student.student_id)
          WHERE Student.student_id like '1'


And please no like '1', it's = '1', but probably student_id is numeric so = 1