Hello.
As far as I know, in Magento you can view products belonging to certain categories if you go to Products -> Categories. Catalog view does not contain categories so you will not be able to filter by this parameter. The same concerns export, default back-end export does not have option to filter by necessary category - it exports all goods.
Actually you can use the workaround: export whole catalog, open the file in any spreadsheet program and for column 'categories' apply filter -
Alternatively you can use extension allowing to export products by categories, like Store Manager for Magento. It is paid, but with 2-week free and fully-functional trial you can cope with the task without any fees.
Here is the tutorial of how it works -
https://www.mag-manager.com/useful-articles/how-to/how-to-export-products-by-category-in-magento/