Two linked selections (Country and Province) that do not link

I will allow myself to comment on some things about your code, in parts.

I wanted to tell you in comment, but space would not give me.

You do not say it in your question, but I guess this code is in a different file than provincias.php

Let's say the file is called paises.php .

Code in paises.php :

1. Do not prepare something already prepared

Prepared queries are used when data is involved from another party. It is not the case here. The query is already prepared , there is no risk of sending it directly using the query method:

$stmt = $conexion -> prepare("SELECT paiscod, paisnom FROM paises ORDER BY paisnom");
$stmt->execute();

Therefore, this would be enough:

$stmt =$conexion->query("SELECT paiscod, paisnom FROM paises ORDER BY paisnom");

2. The whole while procedure you have can be simplified like this:

//Crear un array con los datos
//PDO::FETCH_ASSOC  se usa con fetchAll, no con fetch
$arrDatos = $stmt->fetchAll(PDO::FETCH_ASSOC);

//Verificar si hubo datos. El uso de rowCount para esto es sólo un mito 
//en PDO basta con verificar la respuesta del fetchAll

if ($arrDatos)
{
    //Implementamos una forma más limpia de hacer las cosas
    //Una variable que recoja todo y vaya concatenado

    $strHtml='';
    foreach ($arrDatos as $row)
    {
        if ( $row['paiscod'] == $pais ) 
        { 
            $strHtml.='<option value = "'.$row["paiscod"].' selected>'.$row["paisnom"].'</option>';
        } else {
            $strHtml.='<option value = "'.$row["paiscod"].'>'.$row["paisnom"].'</option>';
        }
     }
     //Fuera del bucle imprimimos la variable concatenada
     echo $strHtml;

 }else{
       echo "No se encontraron países";
 }

3. The script must be in paises.php :

You can improve it, as has been said in comments. I imagine that in HTML you have a select whose id is provincias .

The script, although it may work, is using obsolete code: $(document).ready(function() {... is obsolete from jQuery3. It is recommended to use $(function() {... .

Similarly, Ajax requests are recommended to have at least the ability to handle done in case of success, and fail in case of error ( see here ).

  <script language="javascript">
    $(function() {
        $("#pais").change(function() {
            $("#pais option:selected").each(function() {
                id_pais = $(this).val();
                $.post("provincias.php", {
                    id_pais: id_pais
                }, function(data) {
                    $("#provincias").html(data);
                });
            });
        })
    });
    </script>

The request that is made through Ajax / jQuery must be directed to a different file. In this case it is the file indicated in the url of the request provincias.php .

Code in provincias.php :

$id_pais = $_POST['id_pais'];

$conexion = new Conexion();
$stmt = $conexion -> prepare("SELECT provincod, provinnom FROM provincia WHERE paiscod = :valor");
$stmt->bindParam(':valor', $id_pais);
$stmt->execute();

//Es un error común usar fetch combinado con 'PDO::FETCH_ASSOC'
//Así no se obtiene nada, debes usar fetchAll
//por eso no obtenías las provincias

//Como en países, almacenamos los datos en un arrego
$arrDatos=$stmt->fetchAll(PDO::FETCH_ASSOC))

//Desechamos el mito del rowCount, verificando los datos directamente
//como hicimos en países

if ($arrDatos)
{
    $strHtml="";
    foreach ($arrDatos as $row)
    {

        $strHtml .= '<option value = "'.$row['provincod'].'">'. $row['provinnom'].'</option>';
    }

    echo $strHtml;

}else{

    echo "No se encontraron provincias";

}