How to load custom post archives sub-pages with ajax?

you might use the $.load and preventDefault() from jQuery.

Assugming that you have .page-link link class on each url in pagination and you have all the posts in the #content div following code can help you to load the posts in that div on that particular page.

$("body").on("click", "a.page-link", function(e) {
    e.preventDefault();
    $("#content").load($(this).attr("href") + " #content");
});

This will replace the current posts in that page with the new posts from that particular page. A look on your div structure might help me to write the complete code for you which can work on your site.