Can you have a magical beast as a patronus?

The exact form of the Patronus will not be apparent until the spell has been successfully cast. One of the most powerful defensive charms known to wizardkind, the Patronus can also be used as a messenger between wizards. read more

Yes. Lots of people have magical beasts as a Patronus, according to Pottermore, the official website of Harry Potter. It is rare, though, unless you are unusually familiar with magical beasts (Like Newt), as your Patronus is almost always an animal familiar to you. read more

Patronuses can take the form of magical creatures too - but it is rare. Albus Dumbledore had a Phoenix as his corporeal patronus - not an ordiary animal. So, a partonus can take the form of a Hippogriff, a giant, a hause-elf, a dragon or anything else you can think of. read more