If anyone still struggling with it. Here is the URL for the request to get order from two dates. The issue is the url encode for filter parameter.

https://YOUR-PREST-WEBURL.com/api/orders?filter[date_add]=[2025-01-01%2C2025-01-06]&date=1&output_format=JSON

Below is an working exanple of the PHP cURL to get orders of today date.

// PrestaShop API endpoint (replace with your store's domain)
$prestashop_url = 'https://YOURSHOPURLHERE.com/api/';
// Your PrestaShop API key
$api_key = 'Your API Key';

// Get today's date in the format PrestaShop uses
$today = date('Y-m-d'); // As of today the date will be like '2025-01-06'
// Prepare the URL for fetching orders created today
$order_url = $prestashop_url . 'orders?filter[date_add]=[' . urlencode($today . ' 00:00:00') . ',' . urlencode($today . ' 23:59:59') . ']&date=1&output_format=JSON';

// cURL setup for fetching order IDs
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $order_url); // URL to the orders endpoint
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true); // Return the response as a string
curl_setopt($ch, CURLOPT_HTTPHEADER, array(
    'Authorization: Basic ' . base64_encode($api_key . ':')
));

// Execute the cURL request
$response = curl_exec($ch);

// Check for errors
if (curl_errno($ch)) {
    echo 'Curl error: ' . curl_error($ch);
    exit;
}

// Close the cURL session
curl_close($ch);