Many historic timezones have 15 minute offsets. In the era before American railroads synchronized timezones to the hours, Louisville, KY, as one example close to home, was often UTC-5:45. (It's GE's fault that Louisville and consequently most of the US I-65 corridor wound up EST rather than CST.) I don't expect to win arguments that the city should return to UTC-5:45, but I make them anyway to amuse myself.

And that's the important thing. :-)

Afghanistan is +4:30 , which is different from both Iran and Pakistan

Afghanistan also borders China, and the time jumps three and a half hours at the border.

Most places in Xinjiang have an unofficial local time that they use in addition to official Chinese standard time. See:

https://en.wikipedia.org/wiki/Xinjiang_Time

One can imagine in Kashgar the ridiculousness of Beijing time is even more noticeable than in Urumuqi.

Doesn't really affect things though since there is no road through the Wakhan corridor to reach China, and no road over the mountain pass. If you want to drive it is a very long way via the karakoram highway via Gilgit in Pakistan. Travel from AF to CN is generally done by flying to Dubai, Delhi or Islamabad first.