Step 1: Know the virus biology. Parvovirus B19 has a tropism for erythroid progenitor cells, which explains both its anaemic complications and its characteristic exanthem.
Step 2: Tally the true associations. B19 triggers a transient aplastic crisis when it hits patients with ongoing haemolysis like sickle cell disease, it crosses the placenta early in pregnancy to cause hydrops fetalis, and it is the agent of erythema infectiosum, the slapped-cheek fifth disease.
Step 3: Find the impostor. Roseola infantum, also called exanthem subitum or sixth disease, is a herpesvirus illness caused by HHV-6 (and HHV-7), so it has no link to parvovirus B19.
Step 4: Conclude. The disease not produced by parvovirus B19 is roseola infantum.
\[\boxed{\text{Roseola infantum}}\]