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The Iliad closes with Hector's funeral - this work by Quintus opens with that event before proceeding to continue the story of the Trojan War. It's the only surviving epic from this century.
Written roughly 1200 years after Homer, The Fall of Troy (also called Posthomerica) covers the same ground as some of the lost works in the Trojan War cycle. Did Quintus have access to those works and base his own on them? The introduction to this 1912 Loeb claims that even if he did use those works then the very scanty evidence suggests he completely reworked them. I haven't found more recent scholarship so don't know if that still stands.
(A brief 1879 book by F.A. Paley called Quintus Smyrnaeus and the "Homer" of the Tragic Poets makes a claim that Quintus did draw from the cyclic epics but also that what we know as the work of Homer did as well and what early classical writers called "Homer" was in fact not the texts we know today. I'd guess this claim has not stood up.)
If you're seriously interested in this work then you will probably want to see the new Loeb edition by Neil Hopkinson.
