This depends on what you want to achieve but in general there are hooks.
I am not sure about the posts-widget but I can show you some examples in general.
If you want to add controls to a widget use this (you can find additional information to the names and stuff in their documentation https://developers.elementor.com/add-controls-to-widgets/)
add_action( 'elementor/element/heading/section_title/before_section_end', function( $element, $args ) {
$element->add_control( 'title_color',
[
'label' => 'Color' ,
'type' => \Elementor\Controls_Manager::SELECT,
'default' => 'red',
'options' => [
'red' => 'Red',
'blue' => 'Blue',
],
'section' => 'section_title',
'tab' => 'content',
]
);
}, 10, 2);
the widget in the example is the heading. You can find out the registered names by inspecting the editor or the blocks inside the plugin directory
If you want to change the rendered content of a widget you can use this
add_action( 'elementor/widget/render_content', function( $content, $widget ){ // $content (string) = the rendered content of the widget; widget = the data object
if ($widget->get_name() === 'heading') { // your targeted widget
$settings = $widget->get_settings(); // every that is stored in this method. Titles, captions, margins and so on. Usually this is all you need
// eg if you simply want to wrap your widgets content you can do something like this
$content .= '<div class="i-am-a-wrapper">'.$content.'</div>';
}
return $content;
}, 10, 2 );
I hope this helps :)