How to show recent posts thumbnails on sidebar?

Hi there,

the core WP widget for Recent Posts is really basic - there is no options or filters built into add the images.
You will need a plugin like this:

https://en-gb.wordpress.org/plugins/recent-posts-widget-with-thumbnails/

I just did this, used mentioned plugin (as with my other sites) but when I change size of a thumbnail, nothing changes. I've disabled the cache plugin. Is it somehow related to generate press theme ?

No - GP should not interfere with the plugin settings.