Perhaps Forgotten Colony? That's a series name actually. Author is <PERSON>.
The books in it are:
1. Deliverance
2. Deception
3. Desperation
4. Destruction
5. Declaration
SPOILER ALERT: Everything that follows (till the last couple paragraphs) could easily be considered as giving away far too much. So if someone who is not the poster is reading this, now is a good time to start to scroll slowly, ready to stop quickly...
The idea is an alien species has come to Earth and devastated it. Details in book, but the species is called the Xenotrife. A Marine officer, <PERSON>, has been the most successful unit leader against them, performing mostly extraction missions for a couple years, but the Earth is gone. Turns out what's left of government has created a generation space ship to go elsewhere and reestablish mankind. Or maybe six of them, though <PERSON> only knows of the one he ends up at.
His last mission was to extract a doctor and her team from their own technology recovery mission. She's, shall I say, a piece of work, and a continuing villainess throughout the books.
So, <PERSON> unit is to be security outside the passenger portion of the ship for the 200 years to get to elsewhere, but that goes sour. Things go sour in the ship as well. When they arrive at a star system and planet, it turns out nothing is very democratic anymore in the ship and the current boss is not the man his father and grandfather were. There are enemies on the planet, and guess what? Not coincidentally, thank you old government swine, but the planet has Xenotrife on it. And more.
Shenanigans ensure and eventually everything works out. Works out for the good? For the bad? Hmm...
So:
1. <PERSON>
2. 322
The horrid creature the extracted doctor turns out to be
3. Xenotrife
4. The Xenotrife were engineered for our destruction. There is a whole plan by a universal (not galactic, no, universic, so to speak) "big bad."
5. There's an intermediate level bad guy/good guy species.
If none of that rings any bells, this might not be the book/series you have in mind. If any of it does, well, then it is.
The aliens arrived via probes that landed and disgorged the Xenotrife who began killing humans that survived a disease they also brought (engineered for us)... at least I seem to remember a disease to cull our herd. This matches your description. Additionally, as mentioned below, it turns out the generation ship's destination was chosen by figuring the best backtrack for those probes, turning out to be a planet they call Proxima, and the idea turns out to be that the ship's humans were meant to take the war to the enemy. What they find is not what one would expect and they lost track of that mission completely (not that it was broadly known at all) in the uprising they had along the way. This is also a fine fit to your description.
Caveat: The author has written a lot of books and some of them seem, by series name and kind of material in his blurbs on his website, to be from the same conceptual space. Like one set seems to be people in one of those other ships. That one has a "sheriff" named <PERSON> and the ship is called Pilgrim. If it is related, and "demonic aliens" certainly describes the Xenotrife to a "T" (literally, they were described that way in the above books, first one anyway). If related, probably enough backstory was given to certainly fit your question.
A different series, Forgotten Vengeance, seems to take over after the series described above. The focus seems to be on the "universic" enemy I mentioned as the ultimate bad guys (going up a chain of them...) from that series. Surely the series includes enough backstory to set the stage, so this is the second guess I would make if the <PERSON> series rings no bells. Then (possibly) the <PERSON> series (just above).
Side note: I "bought" them for $0.00 on Amazon (No idea what price the set currently has on Amazon though.) and certainly got my money's worth and more. However, not too much more... I read them all, don't get me wrong, but except for periodic moments, I felt they slowly became a "here's a horrifying immediate death problem, oh here's the planned solution, rinse, repeat, rinse, repeat, rinse, repeat..." kind of thing. 1012