Does The Twilight Zone have anything to do with The War of the Worlds?

Yes, but not directly. The Twilight Zone was an anthology TV series created by Rod Serling. The War of the Worlds was written by HG Wells much earlier. Several stories of The Twilight Zone concerned invasions of earth from other planets, influenced by The War of the Worlds, but it had become a standard science-fiction plot by the time of The Twilight Zone.