SharePoint Content Search webpart filter using Content Type
In source site, create a list.
Create a content type
Assign to a list
crawl the data.
In Source site, create a result source.
Query will be:
path:"https://SP2013" ContentTypeId:0x0100AD11287E5212394CA2F0444231162890*
Or
path:"https://SP2013" SPContentType=MyContentTypeName
In Publishing site create a page
add Content search webpart
Add result source in the query