If im correct you need to add a column(field) in the case related list. This cannot be achieved by using Search Layout. I would suggest you to follow the below steps, Setup-->Account-->PageLayout-->RelatedList. There you find the Related List Properties as i have shown below. There you can add a new column to the related list.
You mean to add a Case field to the Case Related List ??
If im correct you need to add a column(field) in the case related list. This cannot be achieved by using Search Layout.
I would suggest you to follow the below steps,
Setup-->Account-->PageLayout-->RelatedList.
There you find the Related List Properties as i have shown below. There you can add a new column to the related list.
Mark my answer if i answered you.
Thanks,
Sangeetha.