Add custom fields for posts to the search in the wp-admin

search_post_custom_fields.php

<?php
/**
 * Add custom fields for users to the search in the wp-admin
 */
function codepress_search_post_custom_fields( $wp ) {
	global $pagenow, $wpdb;

	// Fill in the post types that should be used
	$post_types = array(
		'post',
		'page'
	);
	
	// Fill in the custom fields you want to add to the search
	$custom_fields = array(
		'my_custom_field_1',
		'my_custom_field_2'
	);

	if ( 'edit.php' != $pagenow || empty( $wp->query['s'] ) || ( ! empty( $post_types ) && ! in_array( $wp->query_vars['post_type'], $post_types ) ) ) {
		return;
	}

	// Search custom fields
	$post_ids = $wpdb->get_col(
		$wpdb->prepare( "
			SELECT DISTINCT p1.post_id
			FROM {$wpdb->postmeta} p1
			INNER JOIN {$wpdb->postmeta} p2 ON p1.post_id = p2.post_id
			WHERE ( p1.meta_key IN ('" . implode( "','", $custom_fields ) . "') AND p1.meta_value LIKE '%%%s%%' )
			",
			esc_attr( $_GET['s'] )
		)
	);

	// so we know we're doing this
	$wp->query_vars['custom_field_search'] = true;

	// Search by found posts
	$wp->query_vars['post__in'] = empty( $wp->query_vars['post__in'] ) ? $post_ids : array_merge( $wp->query_vars['post__in'], $post_ids );
}

add_action( 'parse_query', 'codepress_search_post_custom_fields', 11 );