On January 10, New Hampshire held a special legislative primary for the Carroll County seat 7 district. Even though the Republican ballot listed two candidates, they both lost to a write-in candidate.
See the election returns here.
The general election will be March 10. See this story about the primary.
The reason that they were write-in candidates is because they were not registered in the district. The special election was called rather suddenly due to the incumbent moving out of the district. The filing period was over Christmas week and the people responsible for updating registration records were not available that week (i.e., the office was closed).
The winning write-in candidate had the endorsement of the former representative who was a strong advocate for school choice. One of the on-ballot candidates had stopped actively campaigning and instead endorsed the winner (he was not able take his name off the ballot).
There were actually two write-in candidates. The statewide canvass which the original post linked to, apparently only lists write-in candidates when they win. The town canvasses do include all write-in votes (as a default, New Hampshire always counts cross-over write-in votes), so write-ins for the two Republican on-ballot candidates were counted in the Democratic primary.
The district is three towns in a rural area north of Concord, which itself is a small city. Voting would have been at the town halls in the three towns of the district. In a special election, voters who participated would be seeking to vote in the single race, and likely voting to vote for a particular candidate. At the general election next November, voters will be concentrating on the gubernatorial and congressional elections. They will vote in the legislative race because it is on the ballot.