AddAButtonInSystemConfiguration

ActionCustomButton.php

<?php 

namespace MageVision\Blog56\Controller\Adminhtml\System\Config;

use Magento\Backend\App\Action;
use Magento\Backend\App\Action\Context;
use Magento\Framework\Controller\Result\Json;
use Magento\Framework\Controller\Result\JsonFactory;

class CustomButton extends Action
{
    protected $resultJsonFactory;

    /**
     * @param Context $context
     * @param JsonFactory $resultJsonFactory
     */
    public function __construct(
        Context $context,
        JsonFactory $resultJsonFactory
    ) {
        $this->resultJsonFactory = $resultJsonFactory;
        parent::__construct($context);
    }

    /**
     * @return Json
     */
    public function execute()
    {
        $message = 'Success';
        //Add your functionality

        /** @var Json $result */
        $result = $this->resultJsonFactory->create();

        return $result->setData(['message' => $message]);
    }
}

custom_button.phtml

<script>
    require([
        'jquery',
        'prototype'
    ], function ($) {

        $('#custom_button').click(function () {
            var params = {};
            new Ajax.Request('<?php echo $block->getAjaxUrl() ?>', {
                parameters: params,
                loaderArea: false,
                asynchronous: true,
                onCreate: function () {
                    $('#custom_button_response_message').text('');
                },
                onSuccess: function (transport) {
                    var resultText = '';
                    if (transport.status > 200) {
                        resultText = transport.statusText;
                    } else {
                        var response = JSON.parse(transport.responseText);
                        resultText = response.message
                    }
                    $('#custom_button_response_message').text(resultText);

                }
            });
        });
    });
</script>
<?php echo $block->getButtonHtml(); ?>
<p>
    <span id="custom_button_response_message"></span>
</p>

CustomButton.php

<?php

namespace MageVision\Blog56\Block\System\Config;

use Magento\Backend\Block\Template\Context;
use Magento\Config\Block\System\Config\Form\Field;
use Magento\Framework\Data\Form\Element\AbstractElement;
use Magento\Framework\Exception\LocalizedException;

class CustomButton extends Field
{
    /**
     * @var string
     */
    protected $_template = 'MageVision_Blog56::system/config/custom_button.phtml';

    /**
     * @param Context $context
     * @param array $data
     */
    public function __construct(
        Context $context,
        array $data = []
    ) {
        parent::__construct($context, $data);
    }

    /**
     * Remove scope label
     *
     * @param  AbstractElement $element
     *
     * @return string
     */
    public function render(AbstractElement $element)
    {
        $element->unsScope()->unsCanUseWebsiteValue()->unsCanUseDefaultValue();

        return parent::render($element);
    }

    /**
     * Return element html
     *
     * @param  AbstractElement $element
     *
     * @return string
     */
    protected function _getElementHtml(AbstractElement $element)
    {
        return $this->_toHtml();
    }

    /**
     * Return ajax url for custom button
     *
     * @return string
     */
    public function getAjaxUrl()
    {
        return $this->getUrl('blog56/system_config/customButton');
    }

    /**
     * @throws LocalizedException
     *
     * @return string
     */
    public function getButtonHtml()
    {
        $button = $this->getLayout()->createBlock(
            'Magento\Backend\Block\Widget\Button'
        )->setData(
            [
                'id' => 'custom_button',
                'label' => __('Custom Button'),
            ]
        );

        return $button->toHtml();
    }
}

system.xml

<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
        xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Config:etc/system_file.xsd">
    <system>
        <tab id="magevision" translate="label" sortOrder="1000">
            <label>MageVision Blog Posts</label>
        </tab>
        <section id="blog56" translate="label" type="text" sortOrder="1012" showInDefault="1" showInWebsite="1" showInStore="1">
            <label>Blog Post 56</label>
            <tab>magevision</tab>
            <resource>MageVision_Blog56::blog56_configuration</resource>
            <group id="post" translate="label" type="text" sortOrder="10" showInDefault="1" showInWebsite="1" showInStore="1">
                <label>General</label>
                <field id="custom_button" translate="label comment" type="button" sortOrder="10" showInDefault="1" showInWebsite="0" showInStore="0">
                    <label>Custom Button</label>
                    <frontend_model>MageVision\Blog56\Block\System\Config\CustomButton</frontend_model>
                </field>
            </group>
        </section>
    </system>
</config>

Hello, this code is only for Magento 2.

If you have an example with Magento1 can you send it to me?

Unfortunately we don't have an example.