The component looks for the helper like so:
$helperFile = JPATH_BASE . '/modules/mod_' . $module . '/helper.php';
where $module is the name of your module.
You will have to move the helper.php to modules/mod_modname
The JModelAdmin save() method handles both inserting a single record into a table and updating a single record, and it calls the following Table-related functions:
$table = $this->getTable();
This enables it to get an instance of the Table class - eg for com_content it will be the Content class in libraries/src/Content/Table.php. I'm assuming that you ...