A federal judge’s ruling that a rarely used federal law is unconstitutional has put the Trump administration’s prosecutions of noncitizens accused of voting in federal elections on uncertain ground, with dozens of cases potentially affected. The Justice Department has relied on the statute, which makes voting by noncitizens a crime, as it pursues arrests and charges tied to recent federal elections. The law is now facing legal challenges for the first time, and the judge’s ruling raises questions about whether prosecutors can continue using it. The ruling does not, by itself, establish that every case will be dismissed. But it could significantly weaken the administration’s enforcement campaign, particularly if the decision is upheld or applied broadly. The available details do not identify the judge or explain the ruling’s specific legal reasoning. The legal dispute comes weeks before the Nov. 3 midterm elections, when voters will choose all 435 members of the House and roughly one-third of the Senate. The administration’s campaign has drawn national attention, while the constitutional challenge puts the legal basis for those prosecutions under scrutiny.