Is there any quantum resistant pen-and-paper or mind cipher? I know about VIC and Solitare but as I understand they are not quantum resistant ciphers. Is there any quantum resistant pen-and-paper or mind cipher?
You are not likely to find such a construction. One problem you will run in to is that of size: In order to be secure against brute force search with Grover's algorithm, you will need to use at least 200 bits of secret material. And that assumes you are content with a security level of $2^{100}$.

This is equal to 25 random bytes or a 60 digit long decimal number that you will have to remember and do mental math with. In addition, you will also need to keep your message and any intermediate state in mind as well. 

Assuming that your ciphertexts will be on paper or some other physical medium (because you wouldn't go through the trouble to compute AES by hand to send the result via e-mail), a quantum computer cracking your ciphertext is probably the least realistic of your concerns - if your adversary already has your ciphertext, they probably already have the messages sender and/or recipient as well, which means they have far less expensive ways of obtaining the message.