Looking for a specific cryptosystem (encryption two times with two different keys and then decryption with another different key ) I am looking for a specific cryptosystem with the following properties:

Suppose a User (Say $User_1$) encrypts a message $M$ with the key $K_1$ (the resulted ciphertext is $C_1$). Another user, say $User_2$, encrypts the ciphertext $C_1$ with another key $K_2$ (the resulted ciphertext is $C_2$).
Now, a third user (e.g., $User_3$) should be able to decrypt $C_2$ with the key $K_3$ to achieve the message $M$.

$C_1 = E_{K_1}(M)$

$C_2 = E_{K_2}(C_1)$

$M = D_{K_3}(C_2)$

Note: The keys may be related to each other, but they should be three different keys.
The standard answer to this is the Pollig-Hellman cipher.

Here's how it works; you have a large public prime $p$, and each key $k$ is a value relatively prime to $p-1$.  Then, we have:

$$E_k(M) = M^k \bmod p$$

$$D_k(M) = M^{k^{-1} \bmod p-1} \bmod p$$

What this means is that we have:

$$E_{k_2}(E_{k_1}(M)) = E_{k_1 \cdot k_2 \bmod p-1}(M)$$

So, what you would do is have your TTP generate the three keys $k_1, k_2, k_3$ with $k_3 = k_1 \cdot k_2 \pmod {p-1}$, and you have the relation you're looking for.