You need to work with SharePoint Client Object Model, to download any file from SharePoint site by providing credentials.
Include Microsoft.SharePoint.Client dll reference in your project [No need to install SharePoint]
using Microsoft.SharePoint.Client;
Further you can follow this blog link :
Download all files from SharePoint library
In this blog check
Using Client object model use below code section, This code will download all files. Instead you can put validation for your filename.
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