Nenassa is a world I rescued from its original canon. The basic underlying framework is the same, but I've changed enough of the details that reading the books won't really leave you in much of a position to predict what the setting is like, and I can't really recommend them on their own merits because they don't have many of those.
The story of Nenassa is this:
Once upon a time, there were elves, and they were having a nasty war with one another. The losing side opened a portal to another world and fled through it, which is a wildly dangerous thing to do, but it worked out for them.
On arriving in their new home - which they had no knowledge of or control over before they got there - they found that it was already populated by a native species, humans. Humans had shorter lives and different magic and were overall pretty easy to conquer and enslave, so the elves did that, and methodically exterminated all the magical humans leaving only the powerless ones, and settled in under a unified government with a single Emperor overseeing a landholding aristocracy. (Elven society is just kind of Like That; conquering and enslaving people whenever you have the opportunity to do so is an obvious default for them, not even worth trying to justify any more than you'd bother to justify picking fruit from a tree to eat it.)
Then they found the dragons.
The dragons were powerful, but wildly outnumbered. A dragon caught alone by six elves could usually defeat them without too much hardship; a dragon caught alone by sixty elves was in big trouble. They were very good at sneaking, so good that even at the height of the conflict elven society wasn't totally sure they really existed at all, and eventually they managed to lay low enough that the elves became pretty convinced that even if they had existed once they didn't anymore. This suited the dragons just fine. They hid themselves away in the desert, emerging only in disguise to spy on the elves and play occasional pranks.
Before I go on, I should explain the way magic works for each of these species.
Elves have approximately two types of innate magic: illusioncraft (also known by the older term 'glamourcraft'), and lifecraft.
Illusions range anywhere from a simple visual trick to a fully real physical object, but most elves only have enough power for the low end of that range; it takes a really rare level of magical talent to give illusions even temporary physical form, and only the most powerful of elves can craft an 'illusory' object that is truly real and permanent.
(For most purposes you don't even want true permanence, anyway; as long as an illusion is still not quite fully real, its creator can freely manipulate its form, but making it into a truly real object makes it static and bound by the laws of physics the way real objects are. True conjuration is mostly only useful for creating food, where illusions won't cut it for nutrition however solid and convincing they are, and objects for sale such as clothing or jewelry or architecture, where people will benefit more from guaranteed stability than from something you could still alter or destroy at a whim, and which will eventually fade from existence unless sustained by your attention.)
Portals are an illusion trick: if you form an image of a door to another place, and make it real in the right way, you get an actual door to that place. But they're dangerous, because if you do it wrong, you get a door to an imaginary place that stops existing once the portal is closed or broken, and the only way to tell the difference is to go through and check.
Lifecraft is the ability to manipulate the form and features of living things. Its simplest application is healing, and most elves can do at least a little of that; more advanced applications include things like inducing sensations in a living body, permanently altering a creature's shape or physical attributes, and making those alterations in such a way that they are passed on to the creature's offspring. (The elven study of genetics has been somewhat set back by the fact that they can almost but not quite read and alter gene sequences directly with magic: they have a tendency to think that what they can directly perceive must be, if not the whole story, at least all the important parts.)
The heredity of elven magical power is fairly straightforward: the vast majority of elves are born with a power level somewhere between those of their parents. Occasionally you get a 'wild talent', someone with far more power than either parent; if tendency toward wild talents is heritable, it's not in any way that elves have figured out how to track.
Humans have approximately three types of innate magic: 'sensing', 'moving', and telepathy. (You could bundle in telepathy with sensing and you wouldn't be entirely wrong, but you wouldn't be entirely right, either.)
Sensing includes things like enhanced mundane senses, remote scrying/spying, and some more obscure things like pastwatching or lie detection.
Moving includes telekinesis and teleportation.
Telepathy includes mind-reading, memory-reading, mental communication, and dream-sharing. Some might argue that lie detection belongs more under this umbrella too.
The heredity of human magical power is tricky and complicated. Different aspects of the overall power often come in at very different strengths in a given individual, sometimes with idiosyncratic quirks beyond that, and - most bafflingly from the elven perspective - humans have magic by default, with some genes acting to suppress the innate talent while others amplify it. So even if all magical humans are eradicated, they keep popping up once in a while as the suppression falters from generation to generation through mutations or interactions between different suppressors.
But wait, it gets worse! At some point, an elf tried having kids with a human... and discovered that not only did it work, the resulting offspring were invariably enormously powerful in both forms of magic. Human heritage triggers a strong wild talent in the elven side, and elven heritage unlocks and amplifies human power to an unprecedented degree.
Naturally, elves being the way that they are, they immediately freaked out, killed the scary powerful children, and declared all such hybrids illegal abominations which must be destroyed on sight. It's been long enough since then that many people don't remember exactly why elven-human hybrids are such a bad idea, but they still carry that ingrained revulsion, and anyone familiar with the history will remember the details.
So then there's dragons. Dragon magic comes in approximately three varieties: personal shapeshifting, 'sculpting' (matter manipulation), and a kind of metamagic that allows them to alter magical artifacts they find, move and store magical power, and learn to use any form of magic they have sufficient exposure to even if it's the innate magic of a completely different species.
Dragon magical heredity is also definitely the weirdest of the three kinds involved here. A dragon has a certain level of baseline talent in whatever forms of magic they've picked up and used, and they can develop that talent further by using and exploring the magic, or let it atrophy by ignoring it. During gestation, a dragon passes on to their offspring whatever level of magical ability they've developed - meaning that if you start out with lots of talent at matter manipulation, but never use it, your kids will barely have any, but if you start out with barely any talent at matter manipulation and work on it every day for your whole life, your kids will start with a respectable amount.
The minimum amount of magic that a dragon can pass on to their child is enough shapeshifting to eventually learn how to self-heal and mimic the forms of other species, enough matter manipulation to sculpt stone like clay in one's hands, and enough metamagic to be able to pick up a tiny bit of foreign magic if you spend a lot of time around it and study hard. It's also possible for a dragon to pass on foreign magic to their offspring, but in that case there is no minimum: a dragon can be born with a bit of foreign magic, neglect to develop it at all, and have children who don't get any.
Dragons can shift their sex, and there is some background cultural expectation that a dragon who is especially accomplished at any form of magic will shift female at least long enough to lay an egg or two, but not every dragon is willing to actually do that, whether because they don't want kids or don't want to be pregnant or couldn't stand to be female that long or something else entirely.
Superstition dictates that a dragon with a child on the way should spend the pregnancy actively exercising their magical talents, and that does actually have non-negligible benefits to the child's magical development, but a lot of the specific traditions are just silly; for example, turning yourself into a giant slab of rock and meditating for a day will not give your child enough of a boost to make up for the dangers inherent in a pregnant person temporarily turning themselves into a giant slab of rock.
Now, given that dragons can shapeshift into other species, it's of course possible for a dragon to have children with members of other species. But the heredity of being a dragon works on a similar principle to the heredity of their magic: if you were gestated by a dragon, you're a dragon, and if you weren't, you are not.
That, however, has interesting interactions with what form the dragon takes for gestation and egglaying/birth.
If a dragon were to have children with another dragon and give birth in human form for whatever reason, the baby would be born as a human and need to learn shapeshifting before they could turn into a dragon, but they wouldn't have any more access to human magic than their parent, and once they assumed dragon form for the first time and spent a little while getting used to it they would tend to find it more natural than the form they were born in.
If a dragon were to have children with a member of another species, though... like, just to pick an extra-complicated example, if a dragon assumed a human form and met and fell in love with an elf and then had that elf's child, maintaining human form the whole time...
...well, then the child would be born a dragon in elf-human hybrid form, with all the elven and human magic appropriate to an elf-human hybrid, and all the dragon magic appropriate to their dragon parent. And they might find that their hybrid form felt as much like their 'real' one as their dragon form even once they got comfortable shifting.
Such a child would of course be enormously magically powerful, especially if their dragon parent was any good at magic, which in this case she was.
I am of course talking about the local Miles, and his mother the local Cordelia. The local Piotr is an elven noble, the local Aral is his son and heir, and the local Serg is the Emperor.