How to present a ViewController on Half screen

If you want to present a view controller over half a screen I suggest using the UIPresentationController class it will allow you to set the frame of the view controller when it is presented. A word of advice, this method will stop the user interaction of the presentingViewController until you dismiss the presentedViewController, so if you want to show the view controller over half the screen while retaining user interaction with the presentingViewController you should use container views like the other answers suggested.
This is an example of a UIPresentationController class that does what you want

import UIKit
class ForgotPasswordPresentationController: UIPresentationController{
    let blurEffectView: UIVisualEffectView!
    var tapGestureRecognizer: UITapGestureRecognizer = UITapGestureRecognizer()
    func dismiss(){
        self.presentedViewController.dismiss(animated: true, completion: nil)
    }
    override init(presentedViewController: UIViewController, presenting presentingViewController: UIViewController?) {
        let blurEffect = UIBlurEffect(style: UIBlurEffectStyle.dark)
        blurEffectView = UIVisualEffectView(effect: blurEffect)
        super.init(presentedViewController: presentedViewController, presenting: presentingViewController)
        tapGestureRecognizer = UITapGestureRecognizer(target: self, action: #selector(self.dismiss))
        blurEffectView.autoresizingMask = [.flexibleWidth, .flexibleHeight]
        self.blurEffectView.isUserInteractionEnabled = true
        self.blurEffectView.addGestureRecognizer(tapGestureRecognizer)
    }
    override var frameOfPresentedViewInContainerView: CGRect{
        return CGRect(origin: CGPoint(x: 0, y: self.containerView!.frame.height/2), size: CGSize(width: self.containerView!.frame.width, height: self.containerView!.frame.height/2))
    }
    override func dismissalTransitionWillBegin() {
        self.presentedViewController.transitionCoordinator?.animate(alongsideTransition: { (UIViewControllerTransitionCoordinatorContext) in
            self.blurEffectView.alpha = 0
        }, completion: { (UIViewControllerTransitionCoordinatorContext) in
            self.blurEffectView.removeFromSuperview()
        })
    }
    override func presentationTransitionWillBegin() {
        self.blurEffectView.alpha = 0
        self.containerView?.addSubview(blurEffectView)
        self.presentedViewController.transitionCoordinator?.animate(alongsideTransition: { (UIViewControllerTransitionCoordinatorContext) in
            self.blurEffectView.alpha = 1
        }, completion: { (UIViewControllerTransitionCoordinatorContext) in

        })
    }
    override func containerViewWillLayoutSubviews() {
        super.containerViewWillLayoutSubviews()
        presentedView!.layer.masksToBounds = true
        presentedView!.layer.cornerRadius = 10
    }
    override func containerViewDidLayoutSubviews() {
        super.containerViewDidLayoutSubviews()
        self.presentedView?.frame = frameOfPresentedViewInContainerView
        blurEffectView.frame = containerView!.bounds
    }
}

This also adds a blur view and a tap to dismiss when you tap outside the presentedViewController frame. You need to set the transitioningDelegate of the presentedViewController and implement the

presentationController(forPresented presented: UIViewController, presenting: UIViewController?, source: UIViewController) -> UIPresentationController?

method in there. Don’t forget to also set
modalPresentationStyle = .custom
of the presentedViewController

I find the usage of the UIPresentationController to be a much cleaner approach. Good luck