Yes, you can filter your files and attachments associated with records by simply choosing the appropriate filters.

You can filter your files/attachments by their Name, Created Date, Last Modified Date. 

For Created Date and Last Modified Date, you can choose to have custom date inputs or some pre-selected options like "Last Week" "This Week" etc.

Steps: Goto Mass File Download tab: 

  1. Choose an object.
  2. Choose a list view or search your record having files.
  3. Below that, you will see "Filter For Related Files and Attachments".
  4. Select appropriate Filters for the files/Attachments and hit the Search button.