I'm coming up with a dragonborn character.  Interested if people have any thoughts on if hags might steal a dragonborn child or egg(I guess).  If so would they try and corrupt the soul or use the child in any way? 

This is a question for your DM, not us. But generally, I could certainly see a hag stealing a Dragonborn egg. She’d probably raise the child as her own (think Rapunzel), teaching them some magic and guiding them towards evil. The dragonborn might follow the hag’s teachings and head out to do evil in the world, or run away, knowing they’ll eventually have to confront their “mother.” 

I'm asking to gain knowledge and a concensus or opinion on the subject.  I know I could build my back story however I want but if I could improve my idea with lore I'll try.  Things like would she try to raise the dragonborn is what I'm looking for. Your ideas spark new ones within me🤘👍🤘👍.

Sure.  Hags love stealing and they love corrupting things.  If a hag put its claws on a shiny dragonborn egg, they'd try to raise it.

They'd face two problems in this respect: 1) The egg's clan.  A dragonborn clan will burn down a forest, pulverize a mountain and boil an ocean to get back an egg-napped egg; 2) The inherently noble nature of the dragonborn baby.  Even an evil dragonborn is going to be infallibly courteous and honest and courageous, and a good dragonborn raised by hags would probably spend most of its time trying to reform its surrogate mothers until they wished they'd never seen it.

Thanks for the inspiration. My mind has a story for a dragonborn raised by practitioners of dunamancy but I needed an interesting hook.  How do you remove a dragonborn child from its family and have him raised by wizards.  I'm working it out.

...you mean the Kryn?

You could take some inspiration from Dragonlance, in that setting Takhisis the Queen of Darkness (aka Tiamat) corrupted the eggs of metallic dragons to birth the Draconians. So do a little switcheroo and a Hag coven (who your DM may decide may or may not be in league with Tiamat) killed a metallic dragon and stole its eggs and are now corrupting the eggs to create dragonborn that are loyal to the hag coven. Your character can be one of those dragonborn or may have escaped the corrupting influence and have the goal of rescuing their siblings and liberating them from the Hags thrall.

Quote from Duclaus_Deep >>

Thanks for the inspiration. My mind has a story for a dragonborn raised by practitioners of dunamancy but I needed an interesting hook.  How do you remove a dragonborn child from its family and have him raised by wizards.  I'm working it out.

This is no problem at all.  The youngster showed promise in magical studies and his clan sent him to apprentice with the dunamancers at the age of six.

Another way is to have the parents questing with the egg, something like going to see if the hag has the power to remove a curse or a demonic influence. Either the hag killed the parents or something in the swamp did and she proceeds to raise the child. Maybe the curse or possession still exists? Maybe being raised in a swamp means they are technologically impaired (never seen steel, stone buildings, wagons, money etc) so every thing they come across is a great wonder to behold. 

I think a hag would almost do it to sort of spite a very proud race. Not just egg-nap an egg, but use illusion to maybe replace it with something insulting and then raise the child to be their own. Their history from 4e and 5e I don't think has been explained anywhere very well, but I could see a hag offering the charismatic and loyal dragonborn child to a dark fae patron. Crafting a cunning warlock or a well groomed sorcerer. Maybe even inspire them to be mighty paladin to a Hag's domain? They've seen heroes through the years. A good story for maybe a less than Good aligned, but no less dedicated Paladin to one of the more extreme Paths like Vengeance or Ancients oathed.
Maybe even pushing the mockery bit to an extreme and making the little dragonkin into a barbarian. Utilizing their presence and strength to tarnish the haughty dragonborn clan. The race is described as wearing their hearts on their sleeves. That doesn't necessarily spell naivety, but could mean a youth being raised by an evil presence could be corrupted with little cunning really being utilized.
Lots of stories there. I think the main issue would be "why" but ya know hags are evil and it's something evil feywild denizens would do. Sometimes it's as simple as that.