how to check whether an error occurs due to a specific field in drupal?
This is what you are looking for:

https://api.drupal.org/comment/28464#comment-28464

Edit: Code excerpt from link:

/**
 * Custom Form Validation.
 * Removes all form validation errors caused by a 'foo][bar' form element.
 */
function my_module_form_validate($form, &amp;$form_state) {
  $errors = form_get_errors();
  if ($errors) {
    // Clear errors.
    form_clear_error();
    // Clear error messages.
    $error_messages = drupal_get_messages('error');
    // Initialize an array where removed error messages are stored.
    $removed_messages = array();


// Remove all errors originated by the 'foo][bar' element.
    foreach ($errors as $name =&gt; $error_message) {
      if ($name == 'foo][bar') {
        $removed_messages[] = $error_message;
        unset($errors[$name]);
      }
    }


// Reinstate remaining errors.
    foreach ($errors as $name =&gt; $error) {
      form_set_error($name, $error);
      // form_set_error() calls drupal_set_message(), so we have to filter out
      // these from the error messages as well.
      $removed_messages[] = $error;
    }


// Reinstate remaining error messages (which, at this point, are messages that
    // were originated outside of the validation process).
    foreach (array_diff($error_messages['error'], $removed_messages) as $message) {
      drupal_set_message($message, 'error');      
    }
  }
}