How to set data into session with ajax magento 2

first of all, Magento has five types of sessions :

below is an example of a controller which works when an ajax requests, in that controller I have applied the logic for storing data into the customer session, or if you want any other, please add the comment, i will do so,

Now please find the code below for the controller for the customer session saving:

<?php

 namespace Vendor\Module\Controller\Index;

 use Magento\Customer\Model\Session;
 use Magento\Framework\App\ActionInterface;
 use Magento\Framework\App\RequestInterface;
 use Magento\Framework\Controller\Result\JsonFactory;
 use Magento\Framework\Controller\ResultFactory;


 class Save implements ActionInterface
 {
public $request;
public $session;
public $jsonFactory;
public $resultFactory;

public function __construct(
    Session $session,
    RequestInterface $request,
    JsonFactory $jsonFactory,
    ResultFactory $resultFactory
) {
    $this->session = $session;
    $this->request = $request;
    $this->jsonFactory = $jsonFactory;
    $this->resultFactory = $resultFactory;
}

public function execute()
{
    $customerSession = $this->session->getData();
    $this->session->setSampleName('Mona Lisa');
    $getNames = $this->session->getSampleName();
    $data = $this->session->getData();
    $redirect = $this->resultFactory->create(ResultFactory::TYPE_REDIRECT);
    $params = $this->request->getParams();
    return $redirect->setPath('rma/rma/request');
}
}

And here you will find the data in run time when I'm debugging that it is being saved into the customer session.