I'm actually finally reading the "Harry Potter knockoff" Tanya Grotter and the Magical Double Bass right now in English. It isn't, exactly, by the way. It does offer a lot of similarities but it also has differences which can present us with suggestions.
Harry Potter is actually the latest of a genre of juvenile novels. They have been going on for a long time and they are related to some rather adult books. Thus I find myself reading Tanya Grotter and thinking at one point of Bulgakov's The Master and Margarita (if you are over twelve go out and read it right now. It was a satire on life in the Soviet Union under Scientific Socialism, in which the Devil went to Moscow and was very happy because he didn't believe either. It doesn't "glamorize" Satan or Witchcraft, it just presents the USSR as so satanic it wasn't published till a brief liberalization twenty years after the author's death), on the one hand and Charles Finney's the Circus of Dr. Lao, which is almost a tone poem on the other.
In Juvenile books I recommend Alan Garner's The Weirdstone of Brisingamen and the Moon of Golmroth which depict two ordinary children, Colin and Susan, who fall in with a wizard in Devon named Cadellin Silverbrow, and Susan cooper's The Dark is Rising sequence, the first of which was made into a horrible movie called The Watcher.
One of the characters in the Grotter book is Medusa Gorgonova -- that is Medusa the Gorgon's Daughter. Um. Mythology is fair game. Henry Kuttner, who Rowling sometimes writes like when she is at her best, did a number of fantasies in the forties and fifties with titles like the Mask of Circe and the Dark World which featured characters like Circe or Medea, the Red Witch of Colchis. Grab Bullfinch or Edith Hamilton from your local library. Read them through thoroughly and research characters like the german Nixies and the sirens -- I have a small book of German folklore I literally found after someone discarded it in a free books pile with all kinds of fascinating legends. Rowling definitely did her research. Nicholas Flamel from the first book has been famous for hundreds of years. She is not always accurate but she understands that she is telling an adventure story. So just throw in anything you come across in your reading -- boldly. If you are wrong this is just a story not a research paper.
And that sums it up. You don't have to read everything I mentioned -- certainly Kuttner isn't essential -- but once you understand the context of Rowling's books then what is important is what is magical to you.