However they win, I would guess you have a resisted invasion of the US mainland by German, Japanese and Italian armed forces, prolonged partisan resistance and an attempt by FDR and Truman to hold the line and repel the invasion that is somehow overwhelmed and finally they are killed in the invasion and with the other allies out of commision, US resistance disintegrates to the local level.
I guess there would probably be some kind of Vichy type state, maybe centered in Virginia or somewhere similarly wealthy but bigoted in its cultural attitudes at the time to Nazi Germany. Maybe put Charles Lindbergh or Henry Ford in as the local Marshall Petain equivalent. Have them say America should mind its own business and deal with its internal social, economic and...ethnic problems, stay out of the affairs of Europe and its wars, focus on restoring prosperity and say that the Nazis have brought order to Europe and it would be better to coexist with them than wage a pointless and economically wasteful war that costs American lives and jobs.
The new Fairfax United States we shall call it relegalises the German American Bund, allows Nazi warships to dock in US ports and SS recruitment on US soil as a gesture of "reconciliation and goodwill" to the Third Reich. Nazi troops directly occupy portions of the Northeast but are reduced in number not long after the neutered Axis ally under Lindy or Ford is put in power.
In Pennsylvania Amish communities, Nazi racial hygenicists are sent by the SS and Heinrich Himmler to ascertain the state of their Volkisch kin in America.
The SS officers discretely sent over conclude that though they are ethnic Germans, pure in their Aryan blood, not only does their religion and lifestyle, like other pacifist religious denominations in Germany proper, make them difficult if not impossible to integrate into the Third Reich, but they're...ahem...a little bit...too pure...in their Aryan breeding. At least in the isolated Amish communities in Western Pennsylvania and Ohio they are sent to inspect. In fact they are so pure in their Aryan breeding that at least the Amish they meet with are inbred.
Hitler pawns off the decision on Heydrich, his recently appointed new successor after Goering got a little bit ridiculous and Hess lost his mind and had to be removed though was not killed, who wants to gas them, but decides that it would violate the carefully created illusion of sovereignity he thinks should be cultivated in Fairfax America.
Hitler does not care really, being more concerned with redesigning Berlin, settling ethnic Germans in fortified settlement compounds in the Ukraine, making nice with recently recrowned British sovereign Edward the Eighth, and walking Blondi in the Berchtsgaden, thus the Amish Question is left to Lucky Lindy or Henry Ford, who does the same thing all Americans do with the Amish really...
Ignore them, occasionally buy their handicrafts and drive by them on the road as they ride by you in their horse and buggy and briefly stare, wondering how anyone could live like that and then keep driving.
Though, as American Jews are ghettoized, sterilized and sometimes killed by the new pro-Nazi government, the ancestors of a certain Al Yankovic are killed in 1949 and later so are the ancestors of a certain rap artist named Coolio during the Negro Relocation in the early 1950s, the song "Amish Paradise" is never recorded.