Unfortunately MySQL does not have the handy analytical functions that other SQL languages have. You can simulate them, tough, using some left outer join tricks:
FROM emps t1
LEFT OUTER JOIN emps t2
ON t1.emp_id = t2.emp_id
GROUP BY t1.payment_id,t1.emp_id,t1.cargeTime,t1.payment
This query should get you the last three (more recent) payments per emp_id. Should you need the first three, the AND t1.chargeTime>=t2.chargetime would be written as AND t1.chargeTime<=t2.chargetime.
You can test it here http://sqlfiddle.com/#!2/3c1f9/1/0 Note that I have defined chargeTime as int for fastness sake, but should work with datetimes too.