Unable to display pagination links

I’m trying to generate numbered pagination links on a custom category template. The template displays the current category’s child categories. I’ve pasted the code I’m using below. At the moment there are no links showing and I haven’t been able to work out what’s wrong.

<?php

$total_terms = count( $child_categories );

$pages = ceil($total_terms/$catnum);

// if there's more than one page

if( $pages > 1 ):

    echo '<div class="ft-paginate"><ul class="paginate">';

    // if we're not on the first page, print the previous-link

    if ( $catpage > 1 ) {   

        $prevpage = $catpage - 1;

        if ( $prevpage > 1 ) {  

            echo '<li class="previous-page"><a href="'. get_permalink() .'?paged='. $prevpage .'/"><i class="fa fa-angle-left"></i></a></li>';
        }

        else {

            echo '<li class="previous-page"><a href="'. get_permalink() .'"> &laquo; </a></li>';    

        }

    }

    for ($pagecount=1; $pagecount <= $pages; $pagecount++):

        //set class

        $class = "page-num";

        if ( $pagecount == $catpage ) {

            $class .= " current-page";  

        }

        // print number

        echo '<li class="'. $class .'"><a href="'. get_permalink() .'?paged='. $pagecount .'/">'. $pagecount. '</a></li>';

    endfor;

    // if there is one more page after the current, print the next-link

    if ( $catpage < $pages ) {  

        $nextpage = $catpage + 1;

        echo '<li class="previous-page"><a href="'. get_permalink() .'?paged='. $nextpage .'/"><i class="fa fa-angle-right"></i></a></li>'; 

    }

    echo '</ul>';

    printf( '<span class="total-pages">'. esc_html__( 'Page %1$s of %2$s', 'codilight-lite' ) .'</span>', $catpage, $pages );

    echo '</div>';

endif;

?>

Here is my custom category template with the above pagination code included.

<?php
/**
 * Category Template: Custom
 */

get_header(); ?>
    <div id="content" class="site-content container <?php echo codilight_lite_sidebar_position(); ?>">
        <div class="content-inside">
            <div id="primary" class="content-area">
                <main id="main" class="site-main" role="main">
<?php
        $catpage = get_query_var( 'paged' ) ? get_query_var( 'paged' ) : 1;
            $catnum = 3;
            $offset = ($catnum * $catpage) - 3;

        $cat = get_category( get_query_var( 'cat' ) );
        $cat_id = $cat->cat_ID;
        $child_categories=get_categories(
        array(
        'parent' => $cat_id,
        'orderby' => 'id',
        'order' => 'DESC',
        'hide_empty' => '0',
        'number' => $catnum,
        'offset' => $offset,
        'paged' => $catpage
        // Uncomment the below line if you want empty category to appear on the list.
        // 'hide_empty'   => 0
    )
);
        if (!empty($child_categories)) : $count = 0; ?>

                    <header class="page-header">
                        <?php
                            the_archive_title( '<h1 class="page-title">', '</h1>' );
                            the_archive_description( '<div class="taxonomy-description">', '</div>' );
                        ?>
                    </header><!-- .page-header -->

                    <?php
                        echo '<div class="block1 block1_grid">';
                        echo '<div class="row">';

                    foreach ( $child_categories as $child ){ $count++;
                    include( locate_template( 'template-parts/content-custom.php' ) );

                    if ( $count % 2 == 0 ) {
                                echo '</div>';
                                echo '<div class="row">';
                    }
                    }
                        echo '</div>';
                        echo '</div>';
                    ?>

                <?php else : ?>

                    <?php get_template_part( 'template-parts/content', 'none' ); ?>

                <?php endif; ?>

                <?php

$total_terms = count( $child_categories );

$pages = ceil($total_terms/$catnum);

// if there's more than one page

if( $pages > 1 ):

    echo '<div class="ft-paginate"><ul class="paginate">';

    // if we're not on the first page, print the previous-link

    if ( $catpage > 1 ) {   

        $prevpage = $catpage - 1;

        if ( $prevpage > 1 ) {  

            echo '<li class="previous-page"><a href="'. get_permalink() .'?paged='. $prevpage .'/"><i class="fa fa-angle-left"></i></a></li>';  

        }

        else {

            echo '<li class="previous-page"><a href="'. get_permalink() .'"> &laquo; </a></li>';    

        }

    }

    for ($pagecount=1; $pagecount <= $pages; $pagecount++):

        //set class

        $class = "page-num";

        if ( $pagecount == $catpage ) {

            $class .= " current-page";  

        }

        // print number

        echo '<li class="'. $class .'"><a href="'. get_permalink() .'?paged='. $pagecount .'/">'. $pagecount. '</a></li>';

    endfor;

    // if there is one more page after the current, print the next-link

    if ( $catpage < $pages ) {  

        $nextpage = $catpage + 1;

        echo '<li class="previous-page"><a href="'. get_permalink() .'?paged='. $nextpage .'/"><i class="fa fa-angle-right"></i></a></li>'; 

    }

    echo '</ul>';

    printf( '<span class="total-pages">'. esc_html__( 'Page %1$s of %2$s', 'codilight-lite' ) .'</span>', $catpage, $pages );

    echo '</div>';

endif;

?>

                </main><!-- #main -->
            </div><!-- #primary -->

<?php get_sidebar(); ?>
<?php get_footer(); ?>