Perfectly Normal Beast

Source: Hitchhiker's guide to the galaxy (mostly harmless).

Location: Lamuella, Anhondo Plain

Food benefit: Arthur Dent makes their meat into a rather nice sandwich, and for it he become's "Sandwich Maker" to the people of Lamuella. Some actually call him "Bob's only Begotten Sandwich Maker" which should be a testament to the quality of the sandwich which is made from the meat of the Perfectly Normal Beast. Arthur claims that it is a bit like a cow.

Mysterious property: They migrate in an unexplained way twice a year on the planet of Lamuella before disappearing completely into oblivion.

Old Thrashbarg calls them "Perfectly Normal" Saying that "they come from where they come from, and they go to where they go to, and it's all Bob's will, so it's all perfectly normal".

"Who's "Bob"?"... "Don't ask."

Spoiler: They go to the Domain of "The King", which is apparently their true home.

The Hydra

It would probably be a real bitch to tame. But the reward for doing so is awesome: an essentially infinite supply of hydra heads that grow back near instantly.

(There's probably other mythical creatures with similarly fantastical regeneration/multiplicative abilities, perhaps ones that are less dangerous, but the hydra's the first that came to mind.)

Though it is extremely dangerous, if a Hydra were domesticated (or held in captivity successfully), it does provide enough meat to feed virtually any size population. If you cut off one head, two more grow back immediately, so the Hydra only increases in total head count. Presumably, there is some amount of Hydra neck which also comes with each head, from which several good sized Hydra steaks can be cut. I'd imagine the meat would be a bit like crocodile; probably about halfway between chicken and fish. Obviously, Hydra farming is not for the faint of heart, but considering how much high quality meat could be harvested from a single Hydra in a very short time, it would certainly be worth it.

Griffons and Hippogriffs are obvious candidates for domesticated riding beasts. The ability to fly with a passenger is a pretty good reason to use them.

Medieval Europe and Japan both had lots of stories about domestic fey which would hide around a peasant hut and (in return for small amounts of food left out for it) would do work that benefited the peasants, like repairing furniture or buildings or reaping a field in the night. Certainly no mythology-derived economy would be complete without worker fey.

Dragons are always interesting, not so much as something that is likely to be domesticated, but potentially as something which might be partnered with. Most myths have dragons being as intelligent as humans, and certainly in Western myths, they could often belt out fire hotter than that produced by any forge. The natural outcome of that might be a dragon-powered blast furnace that can produce alloys unavailable anywhere else. Obviously, the dragon would have to benefit from this arrangement, so there would have to be a quid-pro-quo of something they want in return for a few hours blowing into a big stone tower.

Will-o-wisps or pixies kept in jars may be useful sources of light in a pre-electrical setting. Maybe they can be fed with honey, or something equally cheap (though the tales of will-o-wisps usually imply that they "feed" on the dead souls of poor fools who follow their lights into a bog and die).

There are many, many more possibilities...

The Vegetable Lamb of Tartary

An odd Northern European tale says there's a plant that grows in asia with sheep as its fruit. The sheep are very much alive, so it's not all plant - they walk around and graze the grass, attached to the plant by an umbilical cord. The plant and sheep die when the grass runs out, but I suppose you could keep feeding them more grass and get by.

The advantages? You don't have to support livestock except to feed them, which are usually harder to raise than plants and jack up your prices. You don't have to tame them, or watch them carefully so they don't wander away, worry about legendary enclosures for legendary creatures, etc. You just plant, tend, make sure the Big Bad Wolf stays on the appropriate side of your fence, and prune in season!

You'll even get the wool as a bonus. Livestock are good for more than just meat you know!

(In fairness about obscurity: it was at the top of a Wikipedia page. But who doesn't wish mutton grew on trees?)

Humans

(And other humanoids such as elves, orcs etc.)

Outrageous, you say? Wait until I'm done.

It may seem a little evil and inhuman to raise intelligent, sentient beings for food and leather. That's clearly not enough, so use the polymorph spell to make it proper and a lot evil by turning them into actual livestock! And then you can turn them into whatever beast suits your economic needs at the moment.

Advantage over other alternatives: besides having the right cattle for the right time, you solve problems related to POW's, overpopulation, crowded prisons and dissidency, all in one go.

A Cockatrice might pass for a decent farm animal. It is part chicken, which means it probably tasted good. They also lay sizable eggs, which can serve as an additional source of protein.

Of course, a serious economical evaluation—what is the most profitable creature to use as livestock?—should consider feeding and well-being costs specific to the species, which may vary wildly for the same creature in different traditions (something like creature X in tradition Y only mates once per millenium, but in tradition Z it mates on every blue Moon)

Option 1: The Goose That Laid the Golden Eggs assuming you can clone it or get it to reproduce in in some other way and it qualifies as a mythical creature (which arguably does).

Option 2: Unicorns. They can provide both transportation and food. Their horns purify water and have several medical properties, including serving as antipoison. Their tails and blood also have magical properties.