You can use the “File Statistics” REST query the get the file statistics, however, you cannot filter by date using this query.
A solution for this can be by writing a user plugin that will implement a beforeDownload execution point and save the download information in a local file or in a DB schema (e.g. add raw with download by, date, user etc...). Once you have the relevant information, you can have another execution point that will take a start date, stop date, and path as parameters and return the relevant information based on the local file/db information that you generated and saved earlier.