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EDIT: This is the current code that I'm trying to paginate. It creates a custom query that excludes the latest post, as well as all posts from one category. Pagination works fine for the most part, but the problem is that the final link in the pagination list takes me to a blank page.

<section class="card-grid card-grid--push">
    <main class="container container--wide">

    <?php

        $current_page = get_query_var('paged');
        $current_page = max( 1, $current_page );
        $per_page = 3;
        $offset = ( $current_page - 1 ) * $per_page + 1;

        $post_list = new WP_Query(array(
            'cat'            => -15,
            'posts_per_page' => $per_page,
            'paged'          => $current_page,
            'offset'         => $offset, 
            'orderby'        => 'date', 
            'order'          => 'DESC',  
        ));

        if ( $post_list->have_posts() ):
            while ( $post_list->have_posts() ):
                $post_list->the_post();

    ?>

    <a href="<?php the_permalink(); ?>" <?php post_class('card'); ?>>
        <article class="card__content">
            <?php the_post_thumbnail('th-card'); ?>
            <div class="card__head">
                <span class="category">
                    <?php $category = get_the_category(); echo $category[0]->cat_name; ?>
                </span>
                <h2 class="card__title"><?php the_title(); ?></h2>
            </div>
        </article>
    </a>

    <?php endwhile; ?>

    <div class="pagination">

        <?php 
            echo paginate_links( array(
                'total'   => $post_list->max_num_pages,
                'current' => $current_page,
                'type'          => 'list',
                'prev_text' => '?',
                'next_text' => '?'
            ) );
        ?>

    </div>

  <?php  
        endif;
        wp_reset_postdata();
    ?>

</main>

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[EDIT] Here it is, fully tested and working:

$current_page = get_query_var('paged');
$current_page = max( 1, $current_page );

$per_page = 12;
$offset_start = 1;
$offset = ( $current_page - 1 ) * $per_page + $offset_start;

$post_list = new WP_Query(array(
    'cat'            => -15,
    'posts_per_page' => $per_page,
    'paged'          => $current_page,
    'offset'         => $offset, // Starts with the second most recent post.
    'orderby'        => 'date',  // Makes sure the posts are sorted by date.
    'order'          => 'DESC',  // And that the most recent ones come first.
));

// Manually count the number of pages, because we used a custom OFFSET (i.e.
// other than 0), so we can't simply use $post_list->max_num_pages or even
// $post_list->found_posts without extra work/calculation.
$total_rows = max( 0, $post_list->found_posts - $offset_start );
$total_pages = ceil( $total_rows / $per_page );

if ( $post_list->have_posts() ):
    while ( $post_list->have_posts() ):
        $post_list->the_post();


        // loop output here
    endwhile;

    echo paginate_links( array(
        'total'   => $total_pages,
        'current' => $current_page,
    ) );
endif;
wp_reset_postdata();

PS: The code was re-indented using tabs.


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