I wasnt sure if I should put this in the lore forum or not, but here goes. Since dragons have an elemental subtype, can their offspring produce genasi? I want to make a character that has stories and legends of dragons as their forefathers 1000 years or so back, and wanted to know if that would work as a reason why they were born with genasi traits. Did I miss the answer somewhere, or is it impossible?

Short answer is, no lore wise, likely not.

Longer answer: Ehhhh, you might be able to find some wiggle room. Now Genasi like all planetouched HAVE to have Outsider blood, in the case of Genasi Outsider blood from the inner planes (elemental planes). The one circumstance you might be able to make a case for is a Gem Dragon. Although even there it would be a tough sell.

That's what I needed to know. I appreciate it!

I would echo Equalizer in saying that a Genasi wouldn't normally be made from a Dragon, seeing as they are indeed Planetouched and most of the well-known dragons live on the Prime. The subtype doesn't really make them true Elementals, or else they wouldn't need to eat, sleep, or breathe like regular creatures.

But as with most things in D&D, what you want to play is probably already in a rulebook, if you dig enough. Unearthed Arcana has a variant section that outlines Bloodlines. They come in Minor, Intermediate, and Major versions all depending on the type of creature. They're basically a way to represent characters having more passive bloodlines that don't come from not actively investing in classes like sorcerer, elementalist, Dragon Disciple, etc to represent them. I'd explain how they work but you can read it there, and it doesn't really have much bearing on what I'm suggesting next.

While you probably can't get a Fire Genasi from a Red Dragon, maybe you could make a special request to take Fire Genasi and have it represent some sort of passive bloodline? I'm not sure what you really want from the character so it's hard to tell. It's possible to have 1000 year old stories with Elementals being the forefathers, it's possible to have a Fire Genasi who also goes into Red Dragon Disciple due to having small fractions of both bloodlines, or it is possible to have Red Dragon heritage that takes no mechanical changes at all but a few very minor appearance traits. So though it's probably not possible to have a dragon blood spawn a Fire Genasi, there are still many different ways you can approach still having your story if you don't mind shifting a few things around.

_________________