Can a student attendance be marked by any faculty or by the same faculty that has taken the class?

Student attendance can be marked by Admin irrespective of the attendance type that an institution follows. In case of day-wise attendance, group tutor of the respective batch can mark attendance. And if it is of subject-wise type, corresponding faculty can mark attendance for the respective subject. In both cases if you want any other employee to mark attendance, employee must have given Student attendance register privilege.