This name is a synonym of Crataegus uniflora Münchh..
The record derives from RJP
(data supplied on 2011-10-18)
which reports it as a synonym (record 15220) with original publication details: Hortus kewensis Hortus kewensis; 1789 169 1789.
This name record (from RJP) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Crataegus parvifolia in version 1 of The Plant List.