Too often, when people make a story about genocide committed by a fascist government, the story often devolves into a Nazi Germany cliché, especially when the story is set in a modern or futuristic setting. Are there ways to avoid that? I feel it was done so many times that doing so would reduce the value of the novel you're writing.
You need to distinguish allegory and applicability. Tolkien wrote on the subject:
I think that many confuse applicability with allegory, but the one resides in the freedom of the reader, and the other in the purposed domination of the author.
Any time you write about genocide, it would be applicable to the Holocaust to some extent, people would be thinking of the Holocaust to some extent, because the Holocaust is the most prominent point of reference to such an event on people's minds. Even discussing real-life genocides, the Holocaust is mentioned as a point of reference and comparison.
How do you make your story not an allegory of the Nazi regime? You do your research, and then make your story sufficiently different. With fewer similarities, the allegorical interpretation is too weak. To achieve this difference, you might find it helpful to look at other instances of genocide, such as the Armenian Genocide, and other fascist governments, such as Franco's and Mussolini's.
If the victims of the democide are being killed just for being who they are, then getting away from parallels with Nazi Germany is simply not going to happen. The deaths in the Holocaust were not a by-product of some political goal, but were the primary objective of the whole affair.
The massacres caused by the other notorious regimes of history, on the other hand, had different motivations behind them. People were killed as scapegoats, killed for a lack of ideological purity, or killed on the merest suspicion of disloyalty. (It is said that Stalin's purges became so pervasive that from time to time he ordered the death of people who actually deserved it.) Many millions died not from overt malice of any kind, but from the sheer callousness of rulers who were going to push through their precious plan no matter how many people it starved.
Also, there will be more comparisons between your fictional regime and the Nazi regime if you call the fictional one things like fascist, nationalistic, racist, etc., or if its proponents are constantly talking up racial pride. (It is a bit distressing to note that when most people hear the phrase murderous ideology, the first ideology that comes to mind, and often the only ideology that comes to mind, isn't the one with the highest body count.)
So if you don't want your readers thinking, "ah, Nazis" when they read about your evil empire, don't make the regime appear like Nazis.
I wrote a pretty long answer here, which I think applies: Should we avoid writing fiction about historical events without extensive research?
In short - Look at other theories of history, and their theories on fascism/genocide -- maybe those elements aren't linked in certain cultures. Is the fascistic culture being imposed from above - aristocrats consolidating their power, or is it bubbling up from the "little people" in the culture fearing outsiders?
The sidebar on Wikipedia's Fascism page, under "Variants" has many different elements to examine! Fascist Mysticism, Feudal Fascism, EcoFascism... some may have started as mere insults like "Grammar Nazi," but each country that embraced Fascism has done so in different ways.
Most of what it was reacting to was end-of-19th-century issues, but we're solidly into the 21st, so in your stories, society may be reacting to other issues -- not just automation, but even information-centric jobs being outsourced; they had the New Telegraph/Phone linking the world, we have listicle overloads; they had post-industrial revolution companies and a bigger middle class, now corporations are bigger than countries and most families need 2+ earners to approach middle class ...
Probably the best way to see the concerns that a newer fictional fascist society would focus on, would to be to see what Millennials are focused on. (I'm gen-X). Take ideals that you may endorse, but take them to an extreme, perhaps.