Accessing set header cookie across multiple domains

I am working with set header cookies. There is a requirement where my auth service is placed on www.website_one.com and my client sits on www.website_two.com.

Now, ideally, Set-Cookie will not work because it is not allowed but can we do something about this while keeping the web app secure from attacks?

I have tried the

res.cookie("XSRF-TOKEN",    req.csrfToken(),    {        secure: true,        httpOnly: false,        sameSite: 'None',        domain: 'mydomain.com'    });

But this does not work.

I am very curious as to how I can protect my applications if such use cases are to arise.Any help is appreciated, thank you!