I created a custom button "Add" and put in on the related list. But I need some help figuring out how to give it the same functionality of "New" when clicked
Normally I would copy the text from the page over but it's a length page.
If you can't accomplish what you need with the quick action you'll need a lightning component which is much more complicated. You can use Trailhead to learn more about quick actions and lightning components as well.
My other answer, while useful, was base don misunderstanding of the question so I'm posting another answer.
To accomplish what you want you can use a URL hack. Go to the new page for the object you're trying to create and copy the URL, then use that URL as the location for your button.