Here are some synonyms for "dust", depending on the context:

General:

* Powder

* Grit

* Dirt

* Mote

* Soot

* Residue

* Particles

* Specks

* Debris

More specific:

* Fine dust: Powder, pollen, flour

* Coarse dust: Grit, sand, gravel

* Cosmic dust: Stardust

* Household dust: Lint, fluff

* Dust from a fire: Ash, soot, smoke

The best synonym will depend on the specific meaning and context in which you're using the word.