API response to be stored locally

Sure, you can store it in a transient for a day.

<?php
$list_items = get_transient( 'my_list_items' );
if ( false === $list_items ) {
    // Assume "$list_api->get_items()" connects to an API.
    $list_items = $list_api->get_items();
    set_transient( 'my_list_items', $list_items, DAY_IN_SECONDS );
}

if(!empty($list_items)) {
    foreach($list_items as $list_item) {
?>
    <div class="item-container">
        <h2><?php echo $list_item['title']; ?></h2>
        <p><?php echo $list_item['paragraph']; ?></p>
    </div>
<?php
    }
}
?>

References

• get_transient()
• set_transient()