WordPress add_filter to post_date

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' );