wokamoto

You can choose (child) categories and see the posts belong to the chosen category with AJAX.
When the category you choose from the list box has child categories, the child categories will be shown in a new list box. 
Clicking the “Search” button, the list of posts belong to the bottom category which you choose will be displayed under the “Search” button.

Simple Category Search

You can choose (child) categories and see the posts belong to the chosen category with AJAX.

Alexey Golubnichenko

A plugin for WordPress that let you filter posts by taxonomies with AJAX
See the <a href="https://wordpress.org/plugins/agp-ajax-taxonomy-filter/screenshots/" rel="ugc">screenshots</a> and <a href="https://wordpress.org/plugins/agp-ajax-taxonomy-filter/faq/" rel="ugc">FAQ</a> tabs for more details.

AGP Ajax Taxonomy Filter

Plugin working fine, but need little more perfection , like ajax multi-select categories there will be option for choices (Checkboxes,Select Dropdown) for showing filter.now there is simple listing.



Simple Category Search vs AGP Ajax Taxonomy Filter