custom archive links for categories by year

archive-category-year-links.php

// generate custom archive links for current category by year
function get_category_archive_links_by_year($cat_id) {
  global $wpdb;

  // Get years with posts in the current category along with post count
  $years_with_count = $wpdb->get_results(
      "SELECT YEAR(post_date) AS year, COUNT(ID) AS post_count
      FROM $wpdb->posts
      INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id)
      INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)
      WHERE $wpdb->term_taxonomy.taxonomy = 'category'
      AND $wpdb->term_taxonomy.term_id = $cat_id
      AND post_type = 'post'
      AND post_status = 'publish'
      GROUP BY YEAR(post_date)
      ORDER BY post_date DESC"
  );

  $links_with_count = array();
  foreach ($years_with_count as $data) {
      $year_link = get_category_link($cat_id) . '?year=' . $data->year . '&category_name=' . get_category($cat_id)->slug;
      $links_with_count[] = '<a href="' . esc_url($year_link) . '">' . $data->year . ' (' . $data->post_count . ' posts)</a>';
  }

  return $links_with_count;
}

function display_current_category_year_archives_shortcode() {
  $cat_id = get_queried_object_id();
  $category_archive_links_with_count = get_category_archive_links_by_year($cat_id);

  if ($category_archive_links_with_count) {
      $output = '<h2>Posts by Year</h2>';
      $output .= '<ul>';
      foreach ($category_archive_links_with_count as $link) {
          $output .= '<li>' . $link . '</li>';
      }
      $output .= '</ul>';
      return $output;
  }

  return ''; 
}

add_shortcode('category_year_archives', 'display_current_category_year_archives_shortcode');

Create a shortcode: [category_year_archives] that will return a list of category by year archive links.