I think that you only have to change AND with OR in your stament:
IF EXISTS(SELECT 1 FROM HRM.tbAttendanceTimeSlots WHERE (@FromMinutes BETWEEN FromMinutes AND Tominutes) OR (@ToMinutes BETWEEN FromMinutes AND Tominutes))
BEGIN
RETURN -1 --clashing
END
ELSE
BEGIN
INSERT INTO HRM.tbAttendanceTimeSlots
(
FromMinutes, ToMinutes
)
VALUES
(
@FromMinutes,@ToMinutes
)
RETURN 1
END