Comets can produce meteors, but meteors cannot produce comets.
Comets are dusty 'iceburgs' in space and can contain large rocks held together in a matrix of ices.
Once a comet has been by the Sun enough times, it has steadily lost most of its icy material leaving behind a 'dead comet' which consists of rocky material and dust grains clustered near the original head of the comet in its orbit, but also strewn along the comets original orbit. These rocks and dust grains, can enter the Earth's atmosphere if the Earth's orbit happens to intersect the orbit of the comet, and cause meteor showers and fireballs. Not all meteors and fireballs we see, however, come from the larger cometary bodies. Many if not most comes from 'sporadic' sources in the asteroid belt. Meteors are the atmospheric phenomenon we see as bodies enter the atmosphere at high speed, some of these particles can be from comets, and some from other sources in interplanetary space.