iphone 13 green screen death

It sounds like (ad you suspected) the screen is broken.

Do not use third party rescue apps.

If the backup and restore don't work then take ir send it in, though how you do a backup and restore with a busted screen I don't see.

Click here > iPhone Repair & Service - Apple Support 

Or  Click here >  Contact - Official Apple Support 

Anything other than Screen or Battery may be a replacement phone and the price is in the article under "Other damage" 

There is no compensation for hardware that fails during an update. 

Repairs T&C USA

Legal - Apple Repair Terms and Conditions for General Repair - Apple

Repairs T&C UK

Legal - Repair Terms and Conditions - Apple

nithu80 Said:

"iphone 13 green screen death: I have issue with my iphone 13.suddenly went to black screen.first time i try to force restart the phone apple logo appeared same time green and purple virtual little box appeared again goes to black screen.i tried so many ways non of the method is not resolve the issue.i have two more month regular warranty . Ill they fix this issue free"

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Overview a Screenshot:

If iCloud Photos is enabled, then see if you can see this screenshot. See if you see these error in it. If not, then it is an issue with the iOS. If so, then it is a hardware issue, and it is time for a screen. Go Here: Take a Screenshot on your iPhone - Apple Support

nithu80 Said:

"do you have any suggestions for me for this situation?"

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Set this Up Anew:

Being bugs are occurring, then your iPhone, as if you were to sell it. Perform as interacted here, including the backup creation and the iCloud logout.: What to do Before you Sell, Give Away, or Trade in your iPhone, iPad, or iPod touch - Apple Support. Back up what need be, prior to the reset. See if it then works.

If the phone has not been damaged by trauma or water they should fix it under warranty, depends what they find in their diagnostic tests