Do asteroids originally come from debris of star remnants? As we know, asteroids can be found in the Kuiper belt and Oort cloud, but surely the Sun only captures them, not produces them. I know that supernovae may produce heavy elements such as oxygen, silicon and iron, which is the common composition of asteroids, so is it true that asteroids are come from star remnants?
The asteroids (which are mostly found in the asteroid belt between Mars and Jupiter) and more distant, icy bodies found in the Kuiper belt and the Oort cloud were formed at the same time as the rest of the solar system.

The sun and the planets formed from a molecular cloud, containing mostly hydrogen and helium, but also some other elements that came from the remains of stars, including supernovae. This gas cloud collapsed under gravitation to form a star, surrounded by a disk of dust and gas. The matter in the disc formed the planets, and the Kuiper belt. More distant matter in an extended halo around the star, formed the the Oort cloud.

Thus the sun neither captures nor produces asteroids and other solar system bodies. They were formed at the same time as the Sun.

Note "Kuiper" not "Kepler" belt, and the Oort cloud is the source of comets, not asteroids. Asteroids are rocky; Oort cloud bodies are made of ices.