They are just called baby corns as far as I know. Just as with new potatoes, baby or miniature corn is not a special type of corn, it is baby corn — immature little ears of corn, new to this glorious world. It is always some variety of sweet corn, which has not been pollinated, and is harvested within four days of the silks emerging from the ear. (Sweet corn that grows to maturity is usually harvested 20 days after the silks appear).
With baby corn, the cob is eaten — and indeed, if you had to strip the kernels from the cobs, it would take about a zillion kernels and two to three year's labor to make a mouthful.
The industrial production of baby corn has long been the province of Thailand and China — and, indeed, (and we promise not to say, "— and, indeed" again in this article), baby corn has found most widespread use in Asian cooking. But Latin America has recently become another leading source for baby corn.
If you are up to growing corn yourself, you can just as easily grow baby corn. The Virginia Cooperative Extension Service says, "many varieties are suitable, but 'Candystick,' with its 1/4-inch cob diameter at maturity, is a good one to try, especially since it takes up less space in the garden. Harvesting at the right time is tricky; silks will have been produced, but ears not filled out yet. Experimentation is the best way to determine when to harvest baby corn."
If you are more into shopping than farming, you can find baby corn in cans and bottles in the ethnic aisles of well-stocked supermarkets, Asian and Latin markets, and, indeed (drat!) online packed in water, pickled, and spicy pickled.
Cornicus Babitundi Minori or Corn of the toenail of the child crayfishor in binary