I mean as in a city that is not situated at the bottom of the ocean but is not floating on the surface of it either. What would a plausible size and population size be for this kind of construct? Could humans live in such an environment for their whole life? And how deep could such a thing be able to go? I know we(humans) are researching/developing ways to grow food in outer space, so could that technology be used in this as well? And if we can grow vegetables and/or fruit would it be possible for animals to live in the city as well?
The closest thing we build looking like what you describe are nuclear submarines. They can spend a lot of time underwater, taveling around at various depths, and considering their crew they could be seen as small villages.
However they depend on land for their sustenance: supplies, fuel and obviously crew all come from there.
In principle it would be possible to use a nuclear power plant to supply hydroponics and start a food chain on board to supply the crew.
The problem would remain for the nuclear fuel and the spare parts. I doubt that such a thing would have more than a few years of autonomy, at best.