use jQuery.load() to include a php file in a div, wp_query() is part of php file

Using AJAX in WordPress is fundamentally pretty simple.

You need a function that handles the AJAX request, and a couple of add_action calls to map that function to the action you pass to admin-ajax.php, in this case, some_action:

function wpd_ajax_function() {
    get_template_part( 'my-content' );
    wp_die();
}
add_action( 'wp_ajax_some_action', 'wpd_ajax_function' );
add_action( 'wp_ajax_nopriv_some_action', 'wpd_ajax_function' );

This would go in your theme’s functions.php file. You can see that all the function does is load your my-content.php file, and then exits execution.

Once you have that in place, you can test this by visiting admin-ajax.php in your browser with your some_action action appended:

http://yourdomain.com/wp-admin/admin-ajax.php?action=some_action

and you should see your output. If you hit that URL with your jQuery.load() code, you should have everything you need.