The 15-year-old boy hit national headlines this week after a video of him being assaulted at Almondbury Community School last month went viral.
London-based firm Farooq Bajwa and Co wrote to Mr Robinson yesterday in relation to two videos he is said to have posted online.
A message posted on Twitter by lawyer Mohammed T Ankujee shows a letter issued by the law firm to Robinson, whose real name is Stephen Yaxley-Lennon.
The letter, issued yesterday, says: "These videos contain a number of false and defamatory allegations in respect of our client."
It goes on to say that the boy would be pursuing legal action against Mr Robinson and asks that the videos be removed immediately.
According to Metro.co.uk, Mr Robinson later posted a further video in which he admitted to having spread "fake news" about Muslim gangs at the school.
He said he was embarrassed to have been taken in by social media posts from others which now appear to have been untrue.