How get child posts in custom post type by ajax?

To retrieve the post details you have to send the data yourself.

In your JavaScript code you did not send post id.

Update your code like this:

data:{
    action: "applications_filter",
    post_id: current_post_id, //current_post_id should either parsed from DOM or you can write your ajax in PHP file
}

You must need to send post_id before using in php file.

Then you can retrieve via GET

function ajax_applications_filter(){
    $post_id = $_GET['post_id'];

    //Now set post_parent, it will be work
    $products_args = array(
        'post_type' => 'products',
        's' => $search_value,
        'posts_per_page' => -1,
        'tax_query' => $tax_query,
        'post_parent' => $post_id
        //'paged' => $paged
    );
}