Your challenge, should you choose to accept it, is to make sure that the Fascists win World War II, but the Jihadists still rise. The only rule is that the Fascists have to be at war against the Jihadists, as you can see in the title.
Hitler, Bormann, and Goering are killed when the air transport they are taking is downed by a bird strike while flying to Berchtesgaden between June 5th and 10th 1941 (I have no idea if they actually flew together anywhere on this date, but let’s just say they did). The OKW takes control in a military coup over the next several days, executing Himmler, Goebbels, and Ribbentrop. With less than a week to go before D-Day, Operation Barbarossa is canceled (the OKW opposed it in OTL). They pour everything they’ve got into a Mediterranean Campaign and lose it anyway. Britain and the U.S. unceremoniously shove them out of North Africa, but there is no opening to attack the continent. The European War ends with an armistice in late 1943-early 1944. Hostilities end, but a Cold War continues, with the Allies and others backing partisan movements.
One of the places this takes off the most is in the Balkans. Muslim resentment at the Italian rule of Albania in particular boils over. Spying opportunity, the Allies, working through helpful Arab clients, create an international network of Muslims to fight there on the basis of shared religion, funding and training it.
Presto, 1940s al-Qaeda vs. Mussolini and the Nazis.