The 2014 peer-reviewed study by Jesse Richman and others, estimated that from 38,000 to 2.8 million non-citizens voted illegally in the 2008 presidential election with a point estimate of about 1.2 million, meaning about 6.4% of non-citizens voted in the election.
https://ww2.odu.edu/~jrichman/NonCitizenVote.pdf
Critics of this study have decried the very small sample of declared non- citizens on which it is based, 339, about 1% of the sample, without noting that since 4% of the US population are non-citizens, it is likely that many of the respondents who truthfully declared that they voted untruthfully declared that they were citizens. Incredibly, the main criticism of the study’s conclusions take the opposite tack, that in this already undersized sample of non-citizens, most or all who said they voted were actually non-citizens, falsely indicating that they had committed a felony, when actually they hadn’t. You couldn’t make this stuff up and have anyone believe you!