"There's been quite a lot of threatening behaviour from the left, but I am also getting a lot of messages from people who support me," Wilson said.
"My family has found it quite scary. Because you don't know who's making these threats."
But Wilson says he's not been deterred from Twitter and bragged he had gained more than 150 followers in just a few hours since the first article about his identity went up.
"I'm not going off Twitter. They're not going to drive me off Twitter," he said.
Wilson has used the social media site for nine years, posting more than 70,000 messages and on Sunday had 1976 followers and admits he makes comments on the site for "shock value".
The account is laden with criticism of the Prime Minister, frequently using the pejorative nickname "Cindy". On Friday he said he was looking forward to "another great day of triggering the lefties".
Wilson denied being a "troll".
The "Turn Ardern" trend and Wilson's "part-time Prime Minister" comments have been criticised as sexist and anger directed at women in power.
Wilson denies his attacks against Ardern – and his criticism of Ardern appearing on magazine covers - are personal or sexist.
"I don't hate Jacinda Ardern. I've got no like or dislike of her. What I don't like is her performance. Not as a mother, not as a wife, but as a Prime Minister," he said.
A spokesman for Ardern said she wasn't bothered by the magazine turning but had spared a thought for those working in supermarkets - as she had done - spending time turning magazines back around.