get_template_part causes 500 error

The get_template_part() function takes filepath relative to the file it is called in. Do you have a folder called ‘content’ which contains a file content-posttype.php? is the ‘content’ folder located in the same folder as this php file you are calling get_template_part() in?

Also, you can modify your while loop as follows:

        while ( $postsQuery->have_posts() ) {
          $postsQuery->the_post();
          get_template_part( 'content/content', $postType );//please check the file path.
        }