How to add a custom thumbnail size for a specific category?

Put this code on your functions.php

add_action( 'after_setup_theme', 'clonecell_theme_setup' );
function clonecell_theme_setup() {
    /* Set Default Image Sizes*/
    add_image_size( 'mini-thumbnail', 50, 50, true ); // for clonecell recent post widget
}

Or if you already have an action hook on after_theme_setup,put the add_image_size on that function.

Add another add_image_size using this format

add_image_size($name, $width = 0, $height = 0, $crop = false)

Hope this help.