This is for storyboard only.
1) Create a UIViewController (blue) and ctrl + drag (mouse) from your UIBarButtonItem to the UIViewController and select "present as Popover" (like you).
2) Click on the UIViewController (blue) and click on Editor-> embed in the navigation controller (this will be a trick that allows the remaining controller to remain in the pop-up window)
3) Create a second UIViewController (green)
4) Create a UIButton in the first UIViewController (blue) and ctrl + drag the button onto the second UIViewController (green) and select "show"
In the end, it should look like this in the Storyboard:

And the result:


If you want to use PopOver without a navigationBar, you can use it in a blue controller:
self.navigationController?.isNavigationBarHidden = true
, :
@IBAction func backToBlueController(sender: UIButton) {
self.navigationController?.popViewController(animated: true)
}
:
popUp, segue barButtonItem navigationController
-
.

UINavigationController , navigationBar, , .
UINavigationController