Adapt the [[filter if value in list]] to sum column C from the range `my_table!A:C`, return only column C from the filter and wrap the entire function in a `SUM` function. You may want to also add an `IFERROR` to avoid errors when the filter returns an empty range.
```
=IFERROR(SUM(FILTER(my_table!C2:C, COUNTIF(list_sheet!A1:A, my_tableA2:A))))
```
If instead the list is in a single cell, use `SPLIT` to create a dynamic range, splitting the list on the requisite joiner.
```
=IFERROR(SUM(FILTER(my_table!C2:C, COUNTIF(SPLIT(list_sheet!A1, ","), my_tableA2:A))))
```