Screen Time is a great feature in iPhones which lets you/or as parent control time one can spend on the iPhone. You can use family sharing in iPhone and set App limit in your children phone and block the app once the child has reached the limit and after that block the app. But a recent update in iOS now gives an option in ScreenTime “One more minutes” which let the user to access the app for another one minutes and after the one minute is over user again is prompted with “one more minutes” Screen Time option. Allowing "One More Minute" to be selected infinite times effectively renders Screen Time useless.
Many parents are finding this as issue as it defeats the purpose of screen time and there should be a way to disallow bypassing ScreenTime limits. There should be a way Apple should provide to users to disable One more minutes option. Screen time is effectively useless without this function as children just repeatedly tap the 'One more minute' button and go over the allotted time by as much as they want to.
How to turn off “One more minute” Option in ScreenTime on iPhone 11 Pro,XS MAX, 8, 7 plus on iOS 13/13.5 :
There are no updates from Apple on this issue as this is considered as feature and it is unlikely to get fixed as bug. But we have listed some workaround that can disable the one minutes more option in ScreenTime, and hope these fixes/workaround helps you. Please let us know in the comment section
Workaround 1 : Set child age below 13
In the latest iOS 13 version if the child is 13 or older, they get the ‘1 more minute’ option. To disable this you have to login to their apple id account and change their birth year. Change the child age to 12 or younger and they’re still considered a child, so security measures remain and they won’t see one more minute option on screen time. Clearly this approach will require you to create a separate email id for each child.
Workaround 2: set limit for each app to be 12 hours
One other option is set Screentime to be allowed from 7 in the morning to 7 in the evening, also set limit for each app to be 12 hours. Then the option for one more minute will be gone
Workaround 3 : add time limits to one minute on all categories
There is no direct way to stop “One more minute” option in iPhone/iOS 13 but a good workaround is to set up time limits for the apps to one minute then after that you have to block after limit once that’s on the “one more minute” option is no more now and requires to enter in the screen time password that parent has set.

Comments
But I’ve noticed he can only ask for one more minute once, then he needs a passcode the second time. This helps from him asking for one more minute multiple times indefinitely. The downside is he is allowed one more minute for each app separately without a passcode. So then it goes back to defeating the purpose because he will just bounce around every app until he gets bored or used up one minute on every app.