Yes, this is very possible. It has to do with orbital resonances, and quasi-satellites.

The object would have an orbit that looks quite different from Earth, but nearly the exact same orbital period. If the eccentricity is higher, meaning at perihelion it is much closer to the sun than Earth, and Aphelion is much farther, it will appear in the same location of the sky each year. This is called the synodic period.

There are quite a few known asteroids that do this, one is 2014 OL339.

https://catalina.lpl.arizona.edu/css-orbit-view?Namev=2014%20OL339&JDTv=2459873.5&av=0.9988647&Mv=171.06829&ev=0.4608603&Iv=10.18495&Periv=289.69668&Nodev=252.10035&Pv=0.9982975334312787&qv=0&Tv=0&Cx=-112&Cy=512&Cz=852&CZ=194

Notice that if you speed time up on the app, the asteroid is always nearly in the same location of the sky each time Earth passes it.

That would just have to be a comet.

This brings up other issues though. Comets are balls of ice and rock. They tend to cook when they get that close to the sun. The ice will eventually all sublimate away into space leaving a dead comet core behind.

This hypothetical comet would have to have been recently captured into this orbit.

Another issue is the orbit of said comet would not be stable, as when comets heat up and start off gassing, they create jets of gas that can push the comet around. These are called nongravitational forces and they'd likely push the comet out of that orbit after a while.

Quasi-satellites are also unstable configurations.