How to get current user session on SharePoint and call and REST API Net Core with the same authentication data?

Hello,

I have a SharePoint WebPart (I am using SharePoint 2013 On Premise, SharePoint WebPart 2013 and jQuery) and a Net Core REST API (with Windows Authentication enabled). 

I would like to know if there is a way to pass the authentication data  of the current user logged in SharePoint to the rest API. I mean, the final goal is ensure the user (on SharePoint) who is calling the REST API is a valid Windows User.

Thank you!