I vaguely recall reading about a scheme that accomplished this but am not able to figure out which one it was. For the sake of brevity I'm gonna omit any nonces.
Let's say we have an asymmetric keypair: (Kpub, Kpriv)
An observer is provided: C1 = E(Kpub, P1)
P1 is known. It can verified that by performing E(Kpub, P1) the result is indeed C1.
The observer is then provided: C2 = E(Kpub, P2)
P2 is not known to the observer, but they are provided a proof that they can use to verify that C1 and C2 are indeed ciphertexts that can be decrypted by the same private key (or in other words; were obtained by encrypting using the same public key).
I think ElGamal and NIZK were part of the proof but I'm not sure. Any ideas?