Time-zone - Asia/Krasnoyarsk GMT+8
JH - Saturday 0:00
Since the day of the week - Saturday is set on the server, the players' MF is displayed a day later - instead of Friday evening on Saturday evening.

can you please provide a link, or at least screenshots of the server config and the tooltip displayed with false info?
also, what's "a players' MF?"

<startTime>0:00</startTime> <!-- Local server real life time in HH:MM format, when Judgment Hour will start -->
<weekSchedule> <!-- Weekly schedule that configures if Judgment Hour will be active at present day, or not -->
<monday>0</monday>
<tuesday>0</tuesday>
<wednesday>0</wednesday>
<thursday>0</thursday>
<friday>0</friday>
<saturday>1</saturday>
<sunday>1</sunday>
</weekSchedule>
<duration>60</duration> <!-- Judgment Hour duration in real life minutes -->

I can’t set the local time at 24:00,
because the server does not understand this.
My local time GMT+7
MF=JH

That server config equals the time displayed in the tooltip. So what's the issue? I don't get it.
It's saturday and sunday 00:00 both on the livemap and the world xml

In fact JH on Friday and Saturday at GMT 17:00.
Is it possible to check the difference between the local server time and the client time and display the days one day earlier?

saturday/sunday 0:00 in GMT+7 and friday/saturday 17:00 in GMT is the same.
you know how timezones work, right?