The teenager, an 18-year-old boy and 21-year-old man were held as part of a planned counter-terrorism operation on suspicion of terror offences.
They are believed to have links to neo–Nazi group, the Sonnenkrieg Division, which posted a picture of the Duke of Sussex set against a swastika, with a gun pointed at his head and the slogan: "See ya later, race traitor!"
The group is an off shoot of the American Atomwaffen Division, which encourages terrorism and worships Adolf Hitler and Charles Manson.
Searches are currently being carried out at four properties in Bath, London, Portsmouth and Leeds.
The 21-year-old, from Bath, Somerset, was arrested on suspicion of possessing material useful to someone preparing an act of terrorism and conspiracy to inspire racial or religious hatred.
The 18-year-old, from Portsmouth, Hants., was arrested on suspicion of encouraging terrorism and dissemination of terrorist publications.
And the 17-year-old, from London, was arrested on suspicion of encouraging terrorism, dissemination of terrorist publications, and conspiracy to inspire racial or religious hatred.
Sonnenkrieg is thought to have a maximum of 15 members in Britain and Europe.
Meghan's mum Doria is African-American, while her father is Dutch-Irish.
Their difference in skin tone led to the family receiving racial abuse when she was younger.
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