How to set required timezone in LocalTime from joda? Required timezone - Moscow.
Default constructor new LocalTime() shows other time for me: it shows time, which is one hour ahead then in my timezone.

A LocalTime doesn't have a time zone. That's the whole point of it.
If you want the LocalTime for a particular instant in a particular time zone, you can use DateTime and then toLocalTime:
DateTime now = new DateTime(zone); // Urgh: see below
LocalTime localNow = now.toLocalTime();
Note that I would strongly advise having a dependency representing a clock to provide "the current instant" - you can then use a "system" implementation returning the current time via System.currentTimeMillis or the like, but you can also use a "testing" implementation returning a predefined time, allowing you to write unit tests for any moment in time that you like.
With such a dependency, you'd probably have something like:
DateTime now = new DateTime(clock.getCurrentInstant(), zone);
LocalTime localNow = now.toLocalTime();
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