How to create function from code?

You need to pass it at least 2 parameters, or it won’t know what to look for:

<?php
function custom_pagination($cat_id, $catnum) {
    // Start of Pagination
    $total_childs_query = get_categories( array( 'parent' => $cat_id, 'hide_empty' => '0' ));
    $total_terms = count( $total_childs_query );
    $pages = ceil($total_terms/$catnum);
    $base_url = get_term_link( $cat_id, get_query_var( 'taxonomy' ) );

    // if there's more than one page
    if( $pages > 1 ):
        echo '<div class="ft-paginate">';
        echo '<nav class="navigation pagination" role="navigation">';
        echo '<h2 class="screen-reader-text">Posts navigation</h2>';
        echo '<div class="nav-links">';

        // if we're not on the first page, print the previous-link
        if ( $catpage > 1 ) {   
            $prevpage = $catpage - 1;
            if ( $prevpage > 1 ) {  
                echo '<a class="prev page-numbers" href="' . $base_url . '/page/' . $prevpage . '"><i class="fa fa-angle-left"></i></a>';
            } else {
                echo '<a class="prev page-numbers" href="' . $base_url . '"><i class="fa fa-angle-left"></i></a>';  
            }
        }

        for ($pagecount=1; $pagecount <= $pages; $pagecount++):
            //set class
            $class = "page-numbers";
            if ( $pagecount == $catpage ) {
                $class .= " current";   
            }
            if ( $pagecount == $catpage ) {
                echo '&nbsp;<span class="' . $class . '"><span class="screen-reader-text">Page</span>' . $pagecount . '</span>';
            }
            else if ( $pagecount == 1 ) {
                echo '&nbsp;<a class="' . $class . '" href="' . $base_url . '"><span class="screen-reader-text">Page</span>' . $pagecount . '</a>';
            } else {
                echo '&nbsp;<a class="' . $class . '" href="' . $base_url . '/page/' . $pagecount . '"><span class="screen-reader-text">Page</span>' . $pagecount . '</a>';
            }
        endfor;

        // if there is one more page after the current, print the next-link
        if ( $catpage < $pages ) {  
            $nextpage = $catpage + 1;
            echo '&nbsp;<a class="next' . $class . '" href="' . $base_url . '/page/' . $nextpage . '"><i class="fa fa-angle-right"></i></a>';   
        }

        echo '</div>';
        echo '</nav>';

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

        echo '</div>';

    endif;
    // End of Pagination
}
?>

Then, in your template you can use the function adding the values dynamically:

$cat_id = 3;
$cat_num = 5;

custom_pagination($cat_id, $catnum);