Is it possible to add error propagation to OTP? What would be the recipe to add error propagation to a one time pad?
I.e. if I change a single letter in the clear text message, I want
the encrypted message to change starting from that letter and up to the
end of the encrypted message.
What you are actually looking for, which is a way to reuse a one-time pad, is not possible. For OTP reuse to be in any way secure, you need an algorithm with enough "complexity" to be a secure cipher (where the "pad" is actually a key).

For example, in the comments you raise the idea of including a random number and using the 8-bit CBC that Richie Frame and poncho mention. That would not work, because a known plaintext attack would reveal the pad, and the encryption of each byte would only depend on the encrypted value of the previous byte (known) and the pad at that point (recovered after a known plaintext attack).

For the title question the CBC idea is a valid answer, but it does not seem very useful. There is also a complementary question: is there a way to cause changes in the ciphertext to propagate through the plaintext. There e.g. the PCBC mode would work, but again I do not how useful that is.

As for actual suggestions, if you cannot handle the unique pad requirement of OTP (which is common), you should use a conventional cipher like AES. Preferably in authenticated encryption, so that error propagation does not need to be worried about.