[SOLVED] Sorting by modification date
 

How to do it?
I can do it adding
if( have_posts() ) :
// begin of my code >>
if (is_main_query()) :
query_posts($query_string.'orderby=modified');
endif;
// << end of my code
into begin of bfa_loop function (montezuma/includes/template_tags.php file)
but in this case all posts are shown each time not depend on if I select some tag or category. in correct order, but I don't need them all in those cases.

I would use the List Category Posts plugin.

lmilesw, I installed it, but didn't understand how to use it. I got that I should write
[catlist categorypage="yes" orderby=modified]
But where should I put this pseudo-code?

you put shortcodes in posts or pages

In this case this plugin nothing helps me.
If I put this pseudo-code in post or page it really show me list of links to posts with correct order here.
So I can do separate page which can show posts (excerpts are possible as well) with needed conditions.
But I don't need this list. I want to keep current standard behavior of index page - when I can click on tag or on category and it shows filtered posts. Only I need posts previews are sorted by modified date.

you could try making a child theme and using the is_main_query function to change the main query.

You can add the necessary attributes to the shortcode to show full posts, excerpts, images, etc. It might take a bit to understand completely how it works but I believe it will do what you want.

If you can do it with php, you might be able to use the technique shown in this post.

I found the solution:
use this snippet:

just dump this snippet into functions.php