It has happened to me in a previous job.
I've always been told I'm like a machine when I work. If I have a task to get on with, I work through it at immense speed with almost 100% accuracy. I can get more done in one day than most people do in three.
At my old workplace there was a very spoiled and arrogant individual that would argue with everyone to make herself look like the victim, would steal ideas from people and tried to get involved in absolutely everything to make herself look more important than she was. She took a particular dislike to me, because everyone commented on how quickly I worked and it was something she couldn't do better at. I could see her trying, but she never succeeded.
To me there was no competition or race - I was just doing my job, I wasn't there for office competition. I think that frustrated her even more.
Eventually she ended up sitting next to me in the office. She became more friendly after that. People commented on how she seemed to have changed. Then, one day I made a minor mistake - my first - and she jumped straight on it. Clearly she had been watching my computer screen constantly, waiting to see me slip up. She quietly tapped me on the shoulder and pointed out the mistake - I thanked her and fixed it.
A few days later I found out from my manager that she had spoken to my manager about it. She'd gone in saying that the reason I work so fast is because I'm making mistakes, and she gave this example.
Honestly? How did I deal with it? By continuing as I was - I didn't have to be friends with everyone in the workplace, I wasn't trying to compete. I was paid to do a job and I did it. I think the best thing I could have done for dealing with it was to show her that I genuinely didn't care, I wasn't trying to show her up, I was simply better at doing my work than she was.