using claim store the userid globally in asp.net core base contoller

You can use session and check session value in basecontroller. If value of session is not null then read the value from session.

I guess you can check claim in based controller as well.

public abstract class BaseController : Controller
{
string userId = "";
public BaseController()
{
userId = GetUserIdFromClaim(); // check of claim is not null then return the userId
}
}

Check if this can help you.