ambrosite

Post Formats are a theme feature introduced in WordPress version 3.1. This plugin creates a simple widget that lets you place a list or dropdown of post formats in your sidebar. It works much the same as the Categories widget. The Post Formats Widget offers the following options: set a custom widget title, set custom tooltip text, display as a list or as a dropdown, show or hide post counts, show or hide post format ID numbers.
You must have at least one post assigned to a format other than ‘Standard’ in order for this widget to display anything. Note that there is a %format variable you can use in custom tooltip text to output the format name. Also, the format ID refers to the term_id in the wp_terms table. You would not normally want to display the format IDs to your site visitors, however it may be useful to know the IDs during theme development, since Post Formats are just a specialized case of a custom taxonomy.

Ambrosite Post Formats Widget

A list or dropdown of Post Format archives. Works much the same as the Categories widget.

Eduardo Zulian

The Post Format Gallery Widget plugin creates the possibility for you to display images from your galleries inside posts saved under the format ‘Gallery’. You can select the number of images to display, the size of these images, shuffle their orders, the target of links (image file, permalink to attachment, permalink to post or maybe no linking), show captions and use one copy of the basic WordPress style for galleries, which will allow you to set up easily a number of columns.
Important: your theme must support the <a href="https://codex.wordpress.org/Post_Formats#Adding_Theme_Support" rel="nofollow ugc">Gallery post format</a>, otherwise it won’t work.

Post Format Gallery Widget

Display in a widget images from your galleries saved under the post format Gallery.

Ambrosite Post Formats Widget vs Post Format Gallery Widget