Adding a custom property to a Config Entity

example_form.module

<?php

use Drupal\Core\Form\FormStateInterface;
use Drupal\paragraphs\Entity\ParagraphsType;

/**
 * Implements hook_form_alter().
 */
function example_form_form_alter(&$form, FormStateInterface $form_state, $form_id) {
	$form_ids = [
		'paragraphs_type_add_form',
		'paragraphs_type_edit_form',
	];
	if (in_array($form_id, $form_ids)) {
		$attribute = $form_state->getFormObject()->getEntity();
		$form['custom_property'] = [
			'#type' => 'textfield',
			'#title' => 'Custom property',
			'#default_value' => $attribute->getThirdPartySetting('example_form', 'custom_property'),
		];
		$form['#entity_builders'][] = 'example_form_custom_property_form_builder';
	}
}

/**
 * Entity builder for the paragraphs_type config entity.
 */
function example_form_custom_property_form_builder($entity_type, ParagraphsType $custom_property, &$form, FormStateInterface $form_state) {
	if ($form_state->getValue('custom_property')) {
		$custom_property->setThirdPartySetting('example_form', 'custom_property', $form_state->getValue('custom_property'));
		return;
	}
	$custom_property->unsetThirdPartySetting('example_form', 'custom_property');
}

example_form.schema.yml

paragraphs.paragraphs_type.*.third_party.example_form:
  type: config_entity
  label: 'Custom property'
  mapping:
    custom_property:
      type: string
      label: 'Custom property'