Youtube has added a new feature to their website that flags verified Channels. However, I couldn't find anything about it on their API Search. Anyone knows how can I use it on my searches? If not, is it scheduled to be release soon?
You are correct, this is not mentioned in the Youtube API guide. You don't read this from Youtube API because if you check Verfication badgest in Youtube this is more focused on content creators as you need 100k subscribers before you can request to be verified.
Check the Youtube Engineering Blog for announcements or you can file a feature request.