How to set a link to custom archieve page

I am working on my blog where I wish to have a archieve for only
specific category post.

If I understand you, you are doing this wrong. What you want to do is use pre_get_posts to restrict your archives to the one category. Something like this:

function restrict_archives_to_cat($qry) {
  if ($qry->is_main_query() && $qry->is_date()) {
    $qry->set('cat',5); // the category ID you wish to use
  }
}
add_action('pre_get_posts','restrict_archives_to_cat');

I don’t understand the question well enough to get the conditions right, with any confidence. You may have to alter the if conditions to make this work correctly.