In Medieval Mode the Spy keeps two of his three most important mechanics — the Disguise Kit and the Backstab, while the third, the Sapper, is just no longer needed as there are no buildings.
On the other hand, the most important ways of Spychecking, namely the "bite the bullet method" and the Flamethrower are no longer here, so Spychecking is very hard.
Moreover, even if you suspect someone being a Spy or even know that it's a Spy, you can still do practically nothing until you get in melee range. And then you are actually very likely to lose the engagement, because most Spies playing Medieval are very skilled at circling you and langing the deadly Backstab. Going thirdperson works, but in a limited way: circling you is still possible, though not as easily, and your ranged aiming becomes weird, so Snipers and crossbow Medics are greatly endangered.
Against two Spies, you are most likely damned — one of them will get in a backstabbing position. If half the enemy team are Spies, it's possibly better to just leave the server and wait for this to end.
In a normal game, a suspected Spy becomes a dead Spy very soon, or at least loses time to retreat.
How do I actually counter the Spy in Medieval Mode?
Best Answer
As a Spy main, these points hold for fighting Spies in any game mode:
If you take corners wide, you can see this coming and be better placed to avoid it.
This is due to a bunch of weird lag compensation calculations: the game tries to work out where you both actually are, and it may think the Spy is behind you and allow him to backstab, even though on your screen he was clearly in front of you.
Medieval Mode
The majority of the above holds true in Medieval Mode (especially point 2, dueling spies in Medieval is like 90% feign tactics). Here are some more targeted Medieval-mode specific pointers:
These are just some suggestions from my experience, if you need more info there is also the Community Medieval mode strategy guide on the TF2 Wiki, as well as other guides and loadout ideas on Steam, Reddit, and other places as well.