You need to partition your running total by ID. A running total always needs an order of some column, by ordering on which you want to calculate the running total. Assuming running total under each ID is based on ORDER of marks,
Approach 1: It can be written in a simple query if your DBMS supports Analytical Functions
SELECT ID
,name
,marks
,Running_total = SUM(marks) OVER (PARTITION BY ID ORDER BY marks ASC)
FROM students
Approach 2: You can make use of OUTER APPLY if your database version / DBMS itself does not support Analytical Functions
SELECT S.ID
,S.name
,S.marks
,Running_total = OA.runningtotalmarks
FROM students S
OUTER APPLY (
SELECT runningtotalmarks = SUM(SI.marks)
FROM students SI
WHERE SI.ID = S.ID
AND SI.marks <= S.marks
) OA;
Note:- The above queries have been tested MS SQL Server.