I have a game where I play as a half-human/half-dragon fighter and one of my party members just whipped out the question as to if my character is sterile or not. Anyone have a solid answer to this?

Only your GM can have an authoritative answer on this one. (Also, in most games, the question never comes up.) It's their world, so they set the rules of magical reproductive biology if they need them.

I'm pretty sure that, in the lore of the various worlds, that half-elves can have kids, butI have no citations. (I'd try dragonlance, since they had a half-elf character and multi-generation story.) I doubt anything else has been common enough to have an official word.

Thanks!

Think of Draconic Bloodline Sorcerers. They're part-dragon but less than half (uh, unless they are half-dragons, of course), so if they exist, half-dragons must not be sterile.

The question is harder for other hybrids, though, as there's nothing comparable. I know Eberron makes most half-elves come from half-elf families, and that's necessary for the two half-elf Dragonmarked Houses to be a thing, but I'm not aware of anything that important in any other official setting which hinges on one answer or another to this question, nor any specific characters or stories that would cover it.

Obviously if it's a homebrew setting, there's no canon to speak of in the first place, so it's whatever works/whatever your DM says.

(I mean, it's whatever your DM says regardless, but I mean homebrew settings have no canon to even consider, I guess.)

I’m sure I’ve seen references to some D&D half-elves having half-elf parents but I can’t find it at the moment. 

If you want to look at original sources for D&D, then Elrond Half-Elven in LotR is a good example. He has children, so clearly not sterile, and his parents were both half-elves. His father, Earendil, was the son of a human and an elf, whereas his mother, Elwing, was mostly of elven heritage but had a human grandfather (plus a Maia great-grandmother). 

By default, D&D has always treated hybrid characters as perfectly fertile with both other hybrids of the same type as well as their parent races unless explicitly noted as not being the case.  The only examples that come to mind as not being fertile are half-giants and "muls" (half-human/half-dwarves) from the Dark Sun campaign setting.

A side question is, how much "Elven and human" blood does a person need to be a "half-elf"?  I have always made it one-quarter.

In my world, communities of half-elves, or I should say communities with a large segment of half-elves, occur on the human side of the border between human and elven kingdoms.  My one town "designed" for this is Tahgrum.  In Tahgrum, it is the primary road between this human kingdom and the neighboring elven kingdom.  Because this is the main road, all sorts of characters are travelling between the two kingdoms, including all the races found in the world.  Anyone who wants to do business with this elven kingdom will likely pass through Tahgrum.

The elves have strict rules about how to behave in their woods.  They grant a certain degree of freedom to some members of Tahgrum if they show they can be trusted to obey the limits.  Tahgrum has a wide area of farms immediately around it, but also has a well known fur trading enterprise owing to the few members allowed to hunt in the elven forest.  The community is also known for alchemy because they have learned from the elves and can find some unusual ingredients in the woods, as long as they obey the limits.

Naturally some elves find a mate in Tahgrum.  Naturally many of these couple have half-elven children.  The mix of the town is about 3/4 human, 1/6 half-elf and 1/12 elven.  Many half-elves born in Tahgrum choose to stay there, but of the half-elves found elsewhere in the human kingdom, a great majority were born in Tahgrum.  The elves see their spouses die and then they are faced with a decision.  Do they choose to remain and see their children die or do they return to the elven kingdom and live apart from their children and grand children?  Seeing your children and grandchildren die is not the same as seeing your spouse die, so this is a tough decision.

Half-elves face a similar problem if they choose to marry a human.  They will also outlive their spouse and their children, and often their grandchildren.  But they can't return home, so they have to leave Tahgrum if they can't bear the idea of watching your progeny die.

It is an interesting dynamic.

I recently made half demon HALF half elf and want to know if that character is sterile. Demon does not mean tiefling, I mean actual demon monster, like asmodeous or something like that. I also want to know porportions as the demon blood comes from a grandfather. 

Quote from burningkings >>

I recently made half demon HALF half elf and want to know if that character is sterile. Demon does not mean tiefling, I mean actual demon monster, like asmodeous or something like that. I also want to know porportions as the demon blood comes from a grandfather. 

 Ask your GM

Quote from jl8e >>

Quote from burningkings >>

I recently made half demon HALF half elf and want to know if that character is sterile. Demon does not mean tiefling, I mean actual demon monster, like asmodeous or something like that. I also want to know porportions as the demon blood comes from a grandfather. 

 Ask your GM

 I have. Their response was "figure it out, its your character." It seems most hybrids here are fertile so I will have that but I dont have the faintest Idea for porportions of race and even if their would be any likely mutations in the bloodline

Quote from burningkings >>

Quote from jl8e >>

Quote from burningkings >>

I recently made half demon HALF half elf and want to know if that character is sterile. Demon does not mean tiefling, I mean actual demon monster, like asmodeous or something like that. I also want to know porportions as the demon blood comes from a grandfather. 

 Ask your GM

 I have. Their response was "figure it out, its your character." It seems most hybrids here are fertile so I will have that but I dont have the faintest Idea for porportions of race and even if their would be any likely mutations in the bloodline

 There's no science or rules here. The GM's delegated it to you. Do you want it to be?

Okay thats fair, thank you. I will be assuming that the demonic genes are dominant and throw out incomplete and codominance so he will be half demon and 1/4 human and 1/4 elf. Thanks for the help

The real question that should be asked is "is this something that will actually be relevant in the game and does everyone else in the game actually want to be involved in this kind of content?"  Because hearing about your character's fertility or lack thereof is not something that a lot of people are going to want to do while playing D&D.

Me personally prefer to leave a bloodline so when my character dies I can have backup characters. I also think having children is a good extra challenge and can enhance the immersion and rolplaying experience.

Your backup characters don't need to be your own kids.  Heck, most adventurers aren't old enough to have kids that are old enough to be adventurers.

Quote from 6thLyranGuard >>

Your backup characters don't need to be your own kids.  Heck, most adventurers aren't old enough to have kids that are old enough to be adventurers.

 Agreed. Your backup can be your former PC's best friend who now seeks vengeance if someone wants a connection.

Thats true and kids being new characters are just options and friends are also true. You can also just start fresh with brand new characters and lines. Still I stand by the fact that if you are experienced children can also immerse the experience and provide a fun challenge.

In the forgotten realms a half demon half elven being is known as a a Fey’ri and they are fertile  with significant demonic traits passing down at least several generations. Many, but not all, of the Drow are, by lore, “tainted” with demonic “blood” as well and they are fertile. 

Having descendants as backup characters isn’t much of a thing as folks have pointed out. There are really 2 seperate problems:

1) unless you original characters are from 1e - 3.5e they probably aren’t old enough to have adventuring age kids - in FR 4e jumped the timeline by 100 years so elves, dwarves and such could still be around with their descendants and human PCs could have descendants around but be dead in all likelihood. 
2) equiping such  characters is fairly problematic as if the parents were successful enough to survive long enough to raise children to adventuring age they were probably successful nough to have accumulated significant cash and magic resources to equip their children to make them far more survivable. So things like plate/half plate armor, magic weapons and gear etc are possible starting equipment you will have to get your DM to pass on. 
oh  a 3rd thing - if your breeding successors in game sounds like a fairly raunchy game  not a standard game.