The only work I'm aware of that even tried to meaningfully address this was by Richman et al:
Original source for the claim, abstract only.
Link to full paper.
A Washington Post article from the author that addresses critics of the work.
I'm in no position to evaluate the technical merits of the claims, counterclaims, and criticisms on either side of this. What I do know is that the utter belligerence with which people insist that we know this isn't happening seems silly to me and not based on much evidence at all. We haven't really caught much of anyone doing this, but we also don't actually try to catch anyone doing it, especially in the states where it's likely to be the most common.
Another thing I'm fairly confident of is that when people make claims along the lines of "this literally never happens", they're really obviously wrong. Think about it - even if pretty much everyone is well intentioned and not trying to commit election fraud, wouldn't you figure that at least a few people that are ineligible to vote due to citizenship, immigration status, or felonies would accidentally vote just because they weren't aware of what the appropriate laws were? That a country with a hundred million people voting isn't catching anyone doing this accidentally suggests to me that we mostly don't look very hard.
I think it's reasonable to guess that a few hundred thousand illegal votes are likely cast in each election. The standard error on this guess is pretty big, but it's going to be a better guess than, "this literally never happens".