Most of the web applications require Digital Signing documents, files, eReturns (XML or JSON) etc, from user’s Browser using user’s local machine Key-store, USB Token or Smartcard. Older methods being java applets, Active X, etc which are phased out or are being phased out from the new Modern Browser offerings.
Recently much is being talked about WebCrypto API but as of now, WebCrypto API does not provide access to (Windows) or any other Key stores or local crypto USB/Smartcard device.
Although webcrypto does not provide access to smart cards, there is an application called FortifyApp that provides a webcrypto polyfill that does via that same interface.
My company also offers free Signer.Digital Browser Extension for Signing from modern browsers, setup for the same may be downloaded from cNet site https://download.cnet.com/Signer-Digital-Chrome-Extension/3000-33362_4-78042540.html
You would be able to access local systems Certificate Store from Chrome Browser and JavaScript functions in this extension or any other extension available in Chrome Web Store.
Sample ASP.NET MVC Project (Working in VS2015) may be Downloaded
Working implementation may be tested at this portal
Digital Signing from Web Browser