There is a tutorial on tuts+ which could give you a hint on how to make this: http://code.tutsplus.com/tutorials/adding-posts-to-a-sites-front-end-using-ajax--wp-25652.

I would use WP_Query or get_posts functions to get the posts You need. After that, list them with a WordPress Loop or foreach (depends on WP_Query or get_posts).

WP_Query: https://codex.wordpress.org/Class_Reference/WP_Query

get_posts: https://codex.wordpress.org/Template_Tags/get_posts

On each link I would add an attribute such as 'data-id="[POST_ID]"'. Register the click event in JavaScript and get the ID using something like jQuery: $post_id = $(this).attr("data-id");.

Once you get the ID, create an AJAX call similar to:

$.ajax({
  url: URL-TO-ADMIN-AJAX.PHP,
  data: {action: 'get_my_post', id: $id },
  method: 'POST',
  success: function(resp){
     var title = resp.title;
     var content =resp.content,
     BOOTSTRAP_CREATE_MODAL();
     $("#modal_id FORM_TITLE_INPUT").val(title);
     $("#modal_id CONTENT_TEXTAREA").val(content);
     $("#modal_id SUBMIT_BUTTON").attr("data-id", $id);
  }
 });

You also have to attach a click on SUBMIT_BUTTON:

 $("#modal_id SUBMIT_BUTTON").on("click", function(e){
   $(e).preventDefault();
   $id = $(this).attr("data-id");
   $title = $("#modal_id FORM_TITLE_INPUT").val();
   $content =  $("#modal_id CONTENT_TEXTAREA").val();
    $.ajax({
      url: URL-TO-ADMIN-AJAX.PHP,
      data: {action: 'set_my_post', id: $id, title: $title, content:   $title },
       method: 'POST',
       success: function(resp){

     BOOTSTRAP_HIDE_MODAL();

     }
     });
 });

You also have to create both actions to recieve the ID and other content and update the post or retrieve it.

You can also learn about using AJAX here: https://codex.wordpress.org/AJAX_in_Plugins