Let me see if I understand what you are asking... you want to know what kind of traditionally grown vegetable plants put out a regular harvest of edible produce the fastest once mature? If so, here is my input.
A mature summer squash plant can push out a new squash every week when it's in full production. If you have a small patch growing, you can probably pick squash from it a couple of times a week. Greens, like spinach, kales and collards, also push out new leaves pretty continually once they reach a certain size. You can cut from a small patch every few days when they are in full growth. Beans also are pretty fast and pretty prolific in production once they are mature. So, if I wanted continual produce, as quickly as possible, then I'd go for these three: squash, beans and greens. They also have the benefit of not taking long to get to maturity from seed - somewhere around 6 weeks in the case of squash and beans. A bit longer for kale and collards, but if you plant them thickly then you can eat the thinnings while you wait.
Of course, a lot of this depends on how rich your soil is, whether the plants are getting enough sun and enough water, and what season you are in and whether it is that plant's preferred season of growth.
Of course, the very fastest "vegetable" from start to finish (as little as three days) with the capacity to produce a harvest every day once you get a routine started, are sprouts! ;-)