Fixed by adding the below code.
<?php
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$child_query = new WP_Query(array('post_type' => 'blogpost', 'orderby' => 'date', 'order' => 'DESC','paged' => $paged));
while ( $child_query->have_posts() ) : $child_query->the_post(); ?>
<div class="single-post">
<div class="leftContent">
<?php
$image = get_the_post_thumbnail($post->ID,array(300,180));
if($image == ''){
$image = wp_get_attachment_image(11270,array(300,180));
}
?>
<a class="title" href="<?php the_permalink()?>"><?php echo $image; ?></a>
</div>
<div class="rightContent">
<a class="title" href="<?php the_permalink()?>"><?php the_title()?></a><br>
<div class="post-date"><?php the_time('F jS, Y') ?> by <?php echo get_the_author() ?></div>
<div class="content">
<?php echo excerpt($post->ID,320); ?>
</div>
<a href="<?php the_permalink()?>" class="readMore" >Read More</a>
</div>
</div>
<?php
endwhile;
?>
<div class="pagination">
<?php
echo paginate_links( array(
'base' => str_replace( 999999999, '%#%', esc_url( get_pagenum_link( 999999999 ) ) ),
'total' => $child_query->max_num_pages,
'current' => max( 1, get_query_var( 'paged' ) ),
'format' => '?paged=%#%',
'show_all' => false,
'type' => 'plain',
'end_size' => 2,
'mid_size' => 1,
'prev_next' => true,
'prev_text' => sprintf( '<i></i> %1$s', __( 'Newer Posts', 'text-domain' ) ),
'next_text' => sprintf( '%1$s <i></i>', __( 'Older Posts', 'text-domain' ) ),
'add_args' => false,
'add_fragment' => '',
) );
?>
</div>
<?php wp_reset_postdata(); ?>
</div>