Since the MySql ALTER IGNORE TABLE has been deprecated, you need to actually delete the duplicate date before adding an index.
First write a query that finds all the duplicates.   Here I'm assuming that email is the field that contains duplicates.
SELECT
    s1.email
    s1.id, 
    s1.created
    s2.id,
    s2.created 
FROM 
    student AS s1 
INNER JOIN 
    student AS s2 
WHERE 
    /* Emails are the same */
    s1.email = s2.email AND
    /* DON'T select both accounts,
       only select the one created later.
       The serial id could also be used here */
    s2.created > s1.created 
;
Next select only the unique duplicate ids:
SELECT 
    DISTINCT s2.id
FROM 
    student AS s1 
INNER JOIN 
    student AS s2 
WHERE 
    s1.email = s2.email AND
    s2.created > s1.created 
;
Once you are sure that only contains the duplicate ids you want to delete, run the delete.  You have to add (SELECT * FROM tblname) so that MySql doesn't complain.
DELETE FROM
    student 
WHERE
    id
IN (
    SELECT 
        DISTINCT s2.id
    FROM 
        (SELECT * FROM student) AS s1 
    INNER JOIN 
        (SELECT * FROM student) AS s2 
    WHERE 
        s1.email = s2.email AND
        s2.created > s1.created 
);
Then create the unique index:
ALTER TABLE
    student
ADD UNIQUE INDEX
    idx_student_unique_email(email)
;