Just changed it transition.subtype
to kCATransitionFromBottom
transition.subtype = kCATransitionFromBottom
For dismiss the controller.
let transition = CATransition()
transition.duration = 0.5
transition.type = kCATransitionPush
transition.subtype = kCATransitionFromTop
view.window!.layer.add(transition, forKey: kCATransition)
self.dismiss(animated: true, completion: nil)
Please find the below GIF representation.

If you are using the .XIB then please find the below code.
For present the controller.
let newController = NewViewController(nibName: "NewView", bundle: nil)
let transition = CATransition()
transition.duration = 0.5
transition.type = kCATransitionPush
transition.subtype = kCATransitionFromBottom
view.window!.layer.add(transition, forKey: kCATransition)
self.present(newController, animated: true, completion: nil)
For dismiss the controller. It is the same code as above.
let transition = CATransition()
transition.duration = 0.5
transition.type = kCATransitionPush
transition.subtype = kCATransitionFromTop
view.window!.layer.add(transition, forKey: kCATransition)
self.dismiss(animated: true, completion: nil)