Xjyuk

I am currently designing a fantasy world that includes a telekinetic race that can control objects if they are touching its material (they can make flying rocks if they are in the same ground or holding same material). It is way harder for them to control impure materials but they can still control it.

My question is how to imprison them.

Technology a little bit more advanced than Medieval era and magic is mostly used in enchanting.

Edit: their powers are proportional to the amount of matter they touch. So they are more powerful if they have full body armor of that material compared to only a gauntlet of that material.

The walls, floor, and ceiling of the cells are too massive to move or break. The door to the cell is more than two tons and must be slid out of the way for the occupant to get in and out. There is a window to allow passage of meal trays and such.

The door is made of metal embedded in concrete. The concrete is too massive to break apart and that is the only way to get to the metal portion from inside the cell.

The metal is accessible from the outside of the cell (but nowhere near the window, so no reaching of arms) so it is impossible for the prisoner to open the door because s/he can not touch the metal portion. But there are metal handholds on the outside of the cell so guards (who also are telekinetic) can slide the door open (if not all guards are, that's okay, as long as there are a few on every shift).

I recommend similar doors throughout the prison (modern prisons of course have multiple secured doorways). This is far more secure as the prisoner will need to break through multiple security points to escape. An important part of security is the ability for guards to periodically inspect the cells.

Multiple security points also allow prisoners the ability to go take showers, socialize with other prisoners, exercise, etc. Isolation for anything but very brief periods is extraordinarily cruel and destroys the mind; if you want prisoners to be able to function in society after serving their sentences, you need to treat them like human beings and rehabilitate them. This requires movement outside their cells.

For the most difficult prisoners, have cells with doors impossible for one person to move. This requires at least two guards every time the door is opened or closed.

In many societies, including the United States, there are some low-security prisons that are easy to escape. There's also home imprisonment, work release (where the prisoners sleep in the prison), and so forth. It works because the prisoners know when they're caught they will have longer sentences in a less comfy environment. And because they don't want to be on the lam for the rest of their lives; it's mentally exhausting and they will never see their loved ones or lead a normal life. Much easier to just serve your time and be done with it. Of course that isn't the same for people with life (or very long) sentences.

Prisoners who have shown they can not be trusted will be held in more secure prisons, including isolated cells if required.

The most direct security measure is a bunch of guards with guns watching each potential escape route carefully. You may want to incorporate this anyway.

Guns don't have to be ordinary bullets, if that doesn't work on your prisoners, or if you don't want them dead. They can be tranquilizer darts. Or a hallway full of anesthetizing gas. Drag them to a new cell. Start over.

Don't use a mechanism to lock them in at all: Weld the door shut.

The telekinetic abilities have a maximum force level. If there's no locking mechanism to manipulate, then they will have no means of escape other than brute force. If the technology level doesn't permit welding equipment, the same effect can be accomplished with a hot fire and bellows but it will be much slower.

Of course this means that opening and closing the door to the cage will require welding equipment every time, so the cage they are locked in will have to be large enough to live in for 100% of the time. Don't think of it as a jail cell, think animal zoo habitat size.

Impure materials.

From OP:

It is way harder for them to control impure materials but they can
still control it.

Riff on this. I am not entirely sure what impure materials are - some sort of alloy or weird amalgam? But I like it. The cell holding these telekinetiks is maximally impure - maybe made of brick like loaves of metals dust, wood chips, sand, bone, shells, and lots of other things. Different structures would have different impure materials according to what the builders had handy and ease of construction.

House only a few TK in each cell so they can’t work together on the same cell door and locks

alternate construction materials of adjacent cells so groups of cellmates can combine their abilities

As Cyn, described, cell door is massively heavy

Locking mechanism on doors are bars made of different materials, none of which exist inside any cell.

Bars are nested and interpenetrating forming a complex problem like a chinese puzzle box, each lock requiring a unique solution.

The locks and bars are setup such that guards stand on a segment of the lock and have significant mechanical advantage so if they are standing in the right spot, no bars of the locks can move.