首先计算 CTE 中每个月的分数的运行总和.
然后应用您的条件:

First calculate the running sum of the scores for each month in a CTE.
Then apply your conditions:

with cte as (
  select date_format(dateOfExam, '%Y-%m') ExamMonth,
         dateOfExam, score, 
         sum(score) over (partition by date_format(dateOfExam, '%Y-%m') order by dateOfExam) total
  from student
)
select ExamMonth, dateOfExam, score, 
       case when sum(total >= 10) over (partition by ExamMonth order by dateOfExam) = 1 then 'Y' end Reward1,
       case when sum(total >= 20) over (partition by ExamMonth order by dateOfExam) = 1 then 'Y' end Reward2
from cte

请参阅演示.
结果:

See the demo.
Results:

> ExamMonth | dateOfExam | score | Reward1 | Reward2
> :-------- | :--------- | ----: | :------ | :------
> 2020-05   | 2020-05-28 |     5 | null    | null   
> 2020-05   | 2020-05-29 |     5 | Y       | null   
> 2020-05   | 2020-05-30 |    10 | null    | Y      
> 2020-06   | 2020-06-03 |    10 | Y       | null   
> 2020-06   | 2020-06-05 |     5 | null    | null   
> 2020-07   | 2020-07-21 |    20 | Y       | Y      
> 2020-07   | 2020-07-22 |    10 | null    | null   
> 2020-07   | 2020-07-28 |    10 | null    | null