functions.php

<?php
/**
 * Live search
 */
function live_search(){

    $the_query = new WP_Query( [ 
    	'post_type' => ['posts'],
		  'posts_per_page' => -1,
		  's' => esc_attr($_POST['keyword'])
    	]
    );

	if ( $the_query->have_posts() ) {

		while( $the_query->have_posts() ): $the_query->the_post(); ?>
			<li class="live-search-result">
				<a class="live-search-item" href="<?php echo esc_url( post_permalink() ); ?>" title="<?php echo __('Go to','yourtheme') .' '. get_the_title(); ?>">
					<?php if ( has_post_thumbnail() ) {
						the_post_thumbnail('thumbnail');
					} 
					the_title('<h6>','</h6>');
					?>
					</div>
				</a>
			</li>
		<?php

		endwhile;

		wp_reset_query();
		wp_reset_postdata();

	} else {

		?>
		<li class="live-search-result">
			<?php _e('Sorry, the search did not return any results. Try to search with different terms.','yourtheme'); ?>
		</li>
		<?php

	}

  die();
}
add_action('wp_ajax_live_search', 'live_search');
add_action('wp_ajax_nopriv_live_search','live_search');