No, dogs and cats cannot produce a hybrid because they are different species with distinct numbers of chromosomes and different reproductive systems. While there are occasional myths or fictional stories about dog-cat hybrids, they are biologically impossible.
Dogs (Canis lupus familiaris) and cats (Felis catus) belong to different genera within the animal kingdom, and for successful interbreeding, animals generally need to be much closer genetically, typically within the same species or genus. However, it is possible for dogs and cats to coexist peacefully in the same household, but they cannot mate and produce offspring together.