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.

annrra

With this plugin one can easily convert a wordpress posts category into a slideshow of images or just slide through the pages of a category without reloading the pages. 
This can allow you to integrate a small gallery and show posts in a grid layout with their featured images. You can show the plugin inside a particular page or post without writing a single line of code. Simply specify the desired category and number of post shown per page from the settings page of the plugin under “Settings” > “SlidePosts”. If the plugin is used as a gallery each post of the category should have a featured image.

Slide Posts with Ajax Pagination

Adds posts from custom category with ajax pagination

Simple Category Search vs Slide Posts with Ajax Pagination