i want a duck or chick that will stay small does that even exist?

Small ducks only as babies never seen a mini duck sorry now for a small chicken there are several breeds for small .....
Bantams is what these tiny birds are called .. ...
White Cornish;;; A smaller size of the standard cornish
Buff orpington Also a smaller size of standard
RIR same down sized from standard
Buff Brahma same as above
Dominique same as standards
Japanese Bantams my fav;;;; theses are classy little birds a tad prices as well but worth it (I think)
White/Black japanese bantams Mini sizes with large combs short legs and an awesome tail display REALLY (ROOS)
Gray japanese, black tailed buff, black tailed white
Bantams Cochin::
Very nice birds on the stout size short and close to the ground with LOTS of feathers on legs and feet Really neat to have,,, Another from the standard family Cochin.

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Black, Buff, Red, Birchen, White Splash, Barred.Silver Pencile, Golden lace, Blue,
The Bantams d'uccles these are very small with feathered legs very cute
Self blue, Mille Fleur, Porcelain,
Silkie "s another smaller breed of bird alot more feathers Fluffy I call them since they look like fluffy birds real nice as well.
Black, White , Buff, Blue, Splash tiny size well knowen for the extra toe they have and their skin color being almost black ..
Suggest you look at breeds and see what you like best ... Have fun chickens are cool birds to have and keep ,,,,,,

Raise birds and have had several of the above Not the d'uccles

You do get dwarf or bantam ducks, they are about half the size of pekin ducks. They are call ducks and come in different varieties or colours

own call ducks myself

Don't buy a any kind of chick because they all grow up. No such thing as dwarfed ducks.