Custom Group and Fields using API v3
you could try using the latest version of the API explorer to give you an idea of the API call. In general, if the custom field is attached to that entity you can just get it using the custom field number. The custom field number is the ID of the field, eg:

$result = civicrm_api3('Case', 'get', array(
'sequential' =&gt; 1,
'return' =&gt; "custom_315",
'id' =&gt; 1,
));


or REST:

/sites/all/modules/civicrm/extern/rest.php?entity=Case&amp;action=get&amp;api_key=yourkey&amp;key=sitekey&amp;json={"sequential":1,"return":"custom_13","id":1}