Find 13th min value in table group by a column
A quick solution would be to use Row_Number and select for the row number you are interested in.  Something like:

--demo setup
Declare @Table table (ColA int, ColB int);
insert into @Table(ColA,ColB) values
(1,10),
(1,20),
(1,30),
(1,40),
(1,50),
(1,60),
(1,70),
(1,80),
(1,90),
(1,100),
(1,110),
(1,120),
(1,130),
(1,140),
(1,150),
(1,160),
(1,170),
(1,180),
(1,190),
(1,200),

(2,10),
(2,20),
(2,30),
(2,40),
(2,50),
(2,60),
(2,70),
(2,80),
(2,90),
(2,100),
(2,110),
(2,120),
(2,130),
(2,140),
(2,150),
(2,160),
(2,170),
(2,180),
(2,190),
(2,200);

--solution
select * from 
(
select *,ROW_NUMBER() over(partition by ColA order by ColB) as rn
from @Table
) a
where rn = 13;  --The row number you are interested in.




| ColA | ColB | rn |
|------|------|----|
| 1    | 130  | 13 |
| 2    | 130  | 13 |