Is there a plane or experiment plane with props and jets on it?

In a sense there are - there are turboprops which many prop aircraft now use and in a way turbofans (jets) are a kind of combination of props and jets. Turboprops are effectively jet engines but the instead of releasing thrust, the energy is used to turn a prop shaft. A modern turbofan (typical jet engine) has a bypass ratio of 9:1ish where 90% of the air sucked in by the front fan bypassess the core and just comes out the back of the engine producing thrust as a normal prop would.