You need to add an additional filter on the frontend. Very basically it would look like this:
Frontend (eg. single.php):
echo apply_filters( 'my_custom_persian_filter', $post_date );
Backend (eg. functions.php)
function persian_date_function( $date ) {
$date = $converted_to_persian; // there you convert date to persian
return $date;
}
add_filter( 'my_custom_persian_filter', 'persian_date_function' );