Here is a code to get the Quick stats report template with data:
 

<?php
include 'PapApi.class.php';

$session = new Pap_Api_Session("http://URL_to_PAP/scripts/server.php");
if(!$session->login("merchant@example.com", "password")) {
  die("Cannot login. Message: ".$session->getMessage());
}
// more details on session creation here https://support.qualityunit.com/931835-Pap_Api_Session

$request = new Gpf_Rpc_DataRequest('Pap_Merchants_Reports_QuickReportData', 'load', $session);
//$request->setField('isInitRequest', 'Y'); // specifies that the filter you've set under the Quick report as default should be used, without this it displays "All" data
//$request->setField('filterType', 'quick_reports'); // used in conjuction with the above, without this line it won't set the default filter.
//$request->addFilter('userid', '=', '11111111'); // this is how you can specify custom filters, more info about filtering here https://support.qualityunit.com/233666-Gpf_Rpc_GridRequest

try {
  $request->sendNow();
}
catch(Exception $e) {
  die("API call error: ".$e->getMessage());
}

$data = $request->getData();

echo $data->getValue('htmlContent');
?>

If instead of the template you want raw data you can use this approach.