It is, there are a couple of timezones where not only there is a hour difference, but even a 30 and 45 minutes difference. India is UTC +5:30, and Lord Howe Island is UTC +10:30 / +11:00 and New Zealand, Chatham Islands is UTC +12:45 / +13:45, Iran is UTC +3:30 / +4:30 and so on. Where the format is X / Y, that means X is Standard Time, and Y is Daylight time.
Messy.
I think the full list can be found here: https://www.timeanddate.com/time/time-zones-interesting.html
You can use a Bash script that can give you an exhaustive list based on files from /usr/share/zoneinfo/, i.e. find timezones with non-whole hour offsets.
I don’t understand this. What practical difference does it make making the time to round to the nearest quarter of an hour instead of the nearest hour? Personally, I don’t care if noon (sun is in zenith) happens half an hour before 12:00 or half an hour after.
Why do such time zones exist?