It seems the latest time zone is UTC-12, as listed on the Wikipedia UTC time offsets article. But on the iPhone / iPad, I cannot find and choose the time zone of either "Baker Island" or "Howland Island". How could it be done?
IOS – How to set the iPhone / iPad to UTC-12 time zone
It doesn't seem to be possible to set UTC-12 in the Date & Time section in Preferences (see below for more on that).
But I was able to spoof my location with Xcode and a GPS file with these contents:
as explained in Using Xcode to Test Location Services. The Simulator app thought I was on Baker Island (this is a screenshot of the Maps app showing my current location):
This suggests that you could, with the help of a Mac running Xcode, set your iPhone's time zone to UTC-12. I couldn't test it because I don't have a developer account, and one is needed to sign and run apps on an iPhone.
As for the usual method of setting the time with the Date & Time section in Preferences: as I said above that doesn't seem to be possible.
According the Apple support article Get help with the date and time on your iPhone, iPad, and iPod touch, to manually set the time zone you have to "tap Time Zone and enter a city with the time zone that you need".
But Wikipedia's UTC-12 article tells us that UTC−12 is a nautical time zone and although a number of inhabited islands lie within the longitudinal limits of this time zone, none of them keeps the date and time of UTC−12.
So there are no cities to choose, and none of these names (from obvious to obscure) are recognized:
I wonder if turning on "Set Automatically" would properly adjust the time for someone visiting Baker Island...