// THE HTML/PHP

// Categories Nav START
<? $terms = get_terms( array(
    'taxonomy' => 'category-name', // <-- update this
    'orderby' => 'ID',
  )); 
  if ( $terms && !is_wp_error( $terms ) ){ ?>
   <ul class="CHANGEME-categories-nav">
      <? foreach( $terms as $term ) { ?>
        <li id="cat-<?php echo $term->term_id; ?>">
           <a href="#" class="<?= $term->slug; ?> ajax" data-term-number="<?= $term->term_id; ?>" title="<?= $term->name;?>"><?= $term->name; ?></a>
        </li>
      <? } ?>
   </ul>
<? } ?>
// Categories Nav END
                                       
// Results Container START
<div id="CHANGEME-results-container" class="CHANGEME-filter-result">
   <? // post query
     $query = new WP_Query( array(
        'post_type' => 'post-name', // <-- update this
        'posts_per_page' => -1,
      ) ); 
   if( $query->have_posts() ): while( $query->have_posts()): $query->the_post(); ?>
    
      // POST TEMPLATE HERE
    
   <? endwhile; endif; wp_reset_query(); ?>
</div>                      
// Results Container END

// The onpage JS for the page template
<script>
(function($) {
        'use strict';
        function cat_ajax_get(catID) {
            jQuery.ajax({
                type: 'POST',
                url: raindrop_localize.ajaxurl,
                data: {"action": "filter", cat: catID },
                success: function(response) {
                    jQuery("#CHANGEME-results-container").html(response);
                    return false;
                }
            });
        }
        $( ".CHANGEME-categories-nav a.ajax" ).click(function(e) {
            e.preventDefault();
            $("a.ajax").removeClass("current");
            $(this).addClass("current"); //adds class current to the category menu item being displayed so you can style it with css
            var catnumber = $(this).attr('data-term-number');
            cat_ajax_get(catnumber);
        });

    })(jQuery);
</script>
                                       
// Callback function for functions.php or some other functions specific php file like theme.php
// Aside from the inital add actions and a few other things, the actual query and post template should be the same as what is on the page.
                                       
add_action( 'wp_ajax_nopriv_filter', 'CHANGEME_cat_posts' );
add_action( 'wp_ajax_filter', 'CHANGEME_cat_posts' );
                                       
function CHANGEME_cat_posts () {
    $cat_id = $_POST[ 'cat' ];
    $args = array (
	  'tax_query' => array(
		    array(
		      'taxonomy' => 'category-name', // <-- update this
		      'field' => 'term_id',
		      'terms' => array( $cat_id )
		    )
		  ),
	    'post_type' => 'post-name', // <-- update this
	    'posts_per_page' => -1,
	  );
	global $post;
    $posts = get_posts( $args );
    ob_start ();
    foreach ( $posts as $post ) { 
	    setup_postdata($post); ?>

	    // POST TEMPLATE HERE

   <?php } wp_reset_postdata();
   $response = ob_get_contents();
   ob_end_clean();
   echo $response;
   die(1);
}