Custom template Page 2 not working

Please modify your query as:

  $paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
        $posts_per_page = get_option( 'posts_per_page' );

        $artPosts= new WP_Query( array(
                            'post_type'      => 'art',
                            'posts_per_page' => $posts_per_page,
                            'post_status'    => 'publish',
                            'orderby'        => 'title',
                            'order'          => 'DESC',
                            'paged'          => $paged
                            )); 

<?php if ( $artPosts->have_posts() ) : ?>
                        <?php while ( $artPosts->have_posts() ) : $artPosts->the_post(); ?>

// some code for fetching data

 <?php endwhile; ?>
<?php else : ?>
   <div class="col-12">
      <div class="alert alert-info" role="alert"><?php esc_html_e( 'Sorry, we can\'t find any art gallery!', 'artist' ); ?></div>
      </div>
<?php endif; ?>

<div id="pagination">
<?php wpex_pagination($artPosts); ?>
</div>

Put this function in functions.php file of your child-theme.

if ( ! function_exists( 'wpex_pagination' ) ) {

    function wpex_pagination( $query = '' ) {

        $prev_arrow = is_rtl() ? 'fa fa-angle-right' : 'fa fa-angle-left';
        $next_arrow = is_rtl() ? 'fa fa-angle-left' : 'fa fa-angle-right';

        global $wp_query;
        $wp_query = $query ? $query : $wp_query;
        $total = $wp_query->max_num_pages;
        $big = 999999999; // need an unlikely integer

        if ( $total > 1 )  {

             if ( ! $current_page = get_query_var( 'paged' ) ) {
                 $current_page = 1;
            }
            if ( get_option('permalink_structure') ) {
                $format="page/%#%/";
            } else {
                $format="&paged=%#%";
            }

            echo paginate_links( array(
                'base'      => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
                'format'    => $format,
                'current'   => max( 1, get_query_var('paged') ),
                'total'     => $total,
                'mid_size'  => 3,
                'type'      => 'list',
                'prev_text' => '<i class="'. $prev_arrow .'"></i>',
                'next_text' => '<i class="'. $next_arrow .'"></i>',
            ) );

        }
    }

}