I'm pretty sure this was a visual story, on TV, but I could have read it and just imagined strong images to go with it. If I saw it on TV, it'd have been an anthology show, but I've searched and I'm pretty sure it wasn't on any version of The Twilight Zone.
While I'm not strong on details, I remember a man puts together a crystal radio and starts picking up broadcasts from WWII (this is in at least the 1970s). His Father (or uncle?) or some other older male relative was killed in a Nazi attack and he realizes if he can receive signals from WWII, he can send them, so he sends a signal to the past to warn the Allies of the attack where his relative was killed.
The ending is an image I've had in my head for years, but the way my brain works, I could have just imagined it after reading it (if it was a book, and not on TV).
The man wakes up in a bakery or similar small business with his Father running the place and it turns out he saved his relative, but also, in sending that signal, he changed history so the Nazis won WWII and he and his Father have ID cards on and there are swastikas and other Nazi symbols all around, in and outside of their small business, which is somewhere in America, where the Nazis now rule.