How can I create a mine object generation, inside a certain area of position?

To position a part somewhere at random, within a certain rectangular boundary, you could randomly set the x, y, and z component of its position like this:

Ore.Position = Vector3.new(
	math.random(leftBoundary,rightBoundary),
	math.random(bottomBoundary,topBoundary),
	math.random(frontBoundary,backBoundary)
)

Now you mentioned that it's a mining game, so I imagine you'd need to generate the parts to be aligned to a grid. I'm going to assume that that grid size is 4 studs cube. Generally, you'd just have to multiply the position by your grid size, like so:

local gridSize = 4
Ore.Position = Vector3.new(
	gridSize * math.random(leftBoundary,rightBoundary),
	gridSize * math.random(bottomBoundary,topBoundary),
	gridSize * math.random(frontBoundary,backBoundary)
)

Pretty basic, and you'll get parts positioned randomly within the rectangular region defined by the boundaries you'd set.

However, note that this does not check if there is already a part in a certain position, so it's possible to have multiple parts in one spot. This is great for rare ores, but not for regularly occurring ores that need to be placed in chunks, in veins, etc.

The solution for that is another system entirely. Here's how I assume the other games do it:

1. Generate the flat top area of the mine out of stone or dirt or whatever.
2. For every block broken, execute a function that decides what ores (or group of ores) are adjacent to that block, taking into account the height level and rarity of certain ores.

This system is also relatively memory efficient, because you're only generating parts when players break blocks, which is really the only time that they'd get access to those blocks. The mine size only gets bigger and bigger as time goes by. If you want, you could check when the number of blocks nears a certain threshold, then say "the mine will cave in after 40 more blocks are mined", and teleport/kill everyone while the parts are cleared and the mine is reset.

One caveat to this is that you're basically rolling a hypothetical n-sided, weighted dice every time a block is broken: there is no guarantee that you'll get a certain ore at a certain height. If you want that, what you could do is generate a list of ores at certain specific positions, and have your function check if it's already there instead of generating new ores to put in those places. You could create single ores or ore veins this way.

A more complex approach would be to use math.noise, but that's kind of beyond what I could do and explain. Read more about how Minecraft does theirs.

Hope that helps!