Load more posts in the same category – Ajax + Timber

I think there is a small correction in your code, you just passing page number but you have pass category ID also. I’ve added data-category attribute in load more button. So your archive.twig should like:

<section class="archive">
    <p class="archive__title h-headline text-size-l">In the same thematic</p>
    <div id="archive__list" class="archive__list">
        <article class="post">
            ...
        </article>
    </div>
</section>

{% if posts|length >= 10 %}
<section class="cta">
    <a href="#" id="load-more-news" data-category="YOUR_CATEGORY_ID_HERE">
        <p class="cta__text">Load more posts</p>
    </a>
</section>
{% endif %}

Pass data-category attribute value via your script.js, So script.js code should like:

function load_more_news() {
    var page = 1;

    $(document).on('click', '#load-more-news', function(e) {
        e.preventDefault();
        page++;

        $.ajax({
            type: 'POST',
            url: '/wp-admin/admin-ajax.php',
            dataType: 'html',
            data: {
                'action' : 'get_news',
                'get_page' : page,
                'get_category' : $(this).data('category'),
            },
            success: function(data) {
                if($('<div></div>').html(data).find('.archive__item.ended').size() > 0) $('#load-more-news').parents('.cta').remove();
                else $('#load-more-news').parents('.cta').show();
                $('#archive__list').append(data);
            },
            error: function(data) {
                console.log(data);
            }
        });
    });
}

Now receive data-category attribute value in server side like get_page , So your functions.php code should like:

add_action( 'wp_ajax_nopriv_get_news', 'get_news' );
add_action( 'wp_ajax_get_news', 'get_news' );
function get_news() {
    global $post;

    $context = Timber::get_context();
    $context['get_page'] = empty($_POST['get_page']) ? 1 : $_POST['get_page'];
    $context['get_category'] = isset($_POST['get_category']) ? $_POST['get_category'] : '';

    $context['posts'] = Timber::get_posts(array(
        'post_type' => 'post',
        'post_status' => 'publish',
        'category__in' => array($context['get_category']),
        'posts_per_page' => 10,
        'paged' => $context['get_page'],
        'has_password' => FALSE
    ));
    $count = count(Timber::get_posts(array(
        'post_type' => 'post',
        'posts_per_page' => -1,
        'post_status' => 'publish',
        'category__in' => array($context['get_category'])
    )));

    if($count <= $context['get_page'] * 10) $context['ended'] = 'ended';

    Timber::render( 'bloc_news.twig', $context );

    die();
}