L. Frank Baum seemingly didn't think of Ozma as a fairy initially, but gradually bestowed this status upon her. I know The Emerald City of Oz mentions her fairy wand, and later books show her using fairy magic. In a conversation in Glinda, the Supreme Dictator of the Flatheads tells the Royal Ruler, "If you are really Princess Ozma of Oz...you are one of that band of fairies who, under Queen Lurline, made all Oz a Fairyland. I have heard that Lurline left one of her own fairies to rule Oz, and gave the fairy the name of Ozma." But if she's a fairy from Lurline's band, is she still the daughter of the last King of Oz? Jack Snow addressed this issue in Magical Mimics, in which Lurline left the baby fairy Ozma with the old and childless King Pastoria, intending that she inherit the throne. So Ozma is one of Lurline's fairies, and also Pastoria's legal adopted child.
There are still questions remaining, however. The first sentence of Chapter 22 of Magic reads, "It seems odd that a fairy should have a birthday, for fairies, they say, were born at the beginning of time and live forever." Both Kabumpo and Wishing Horse say that Ozma is a thousand years old. And Merry Go Round has Ozma recognizing the Unicorn of Halidom from when she lived in the fairy forest of Burzee. So did she spend centuries as a baby fairy before being taken to Oz? I guess that's possible, as we don't know how quickly fairies develop. Indeed, it's odd that an immortal race would even HAVE children, but Baum shows his immortals trying a lot of different things out of boredom. This brings us to a curious statement in Scarecrow, which says that Ozma was "[b]orn of a long line of Fairy Queens." Even if some fairies do choose to have children, why would there be any need for such a line if fairies never die? Sure, they could have abdicated or been enchanted, but even if this had happened to a few of them, would it have been the case for an entire "long line"? Perhaps these queens were not FULL fairies, but simply had some fairy blood. That wouldn't explain how Ozma herself is apparently a full fairy, however. Perhaps we'll just have to accept that not all of the legends about the Queen of Oz are true, regardless of whether the Royal Historians reported them as such.
Throughout the course of the series, Ozma is given a few fairy relatives. In Tik-Tok, the Royal Gardener of the Rose Kingdom claims that a not-yet-picked princess "is named Ozga, as she is a distant cousin of Ozma of Oz." Betsy Bobbin and the Shaggy Man pick the princess, but as the roses want a male ruler, they drive Ozga out with the strangers. While she's a flower fairy in her own kingdom, she becomes mortal upon leaving. Eventually, she and Jo Files of Oogaboo fall in love, and she goes back to Oz with him. Actually, in the play on which the book Tik-Tok is based, the Rose Princess is named Ozma, but Baum obviously couldn't keep that name when he brought the character into the main series. The general belief is that the "ma" in "Ozma" came from Baum's wife's name Maud, the "ga" came from her maiden name, Gage. So how is a flower fairy related to Ozma of Oz? Baum never gave an explanation, but Melody Grandy did. In her Seven Blue Mountains trilogy, it's stated that the royalty of the Rose Kingdom are descended from a fairy named Omiarr, who was turned into a rosebush by an evil magician.
Another relative, Princess Ozana, is introduced in Magical Mimics. She is the Guardian of Oz, whose job is to keep the fairyland safe from the evil Mimics. While she initially keeps watch from the Mimics' own home at Mount Illuso, Ozma later transports her and her home to Story-Blossom Mountain in the Quadling Country. Oddly enough, the story of Lurline leaving Ozana at Illuso mentions the Guardian's "fairy wings," but she doesn't appear to have these when she actually shows up in the main story.