Enischnomyia stegosoma was described based on a single fossilised specimen which is preserved as an inclusion in a transparent chunk of Dominican amber.

[1] The amber is fossil resin that was produced by the extinct Hymenaea protera, which formerly grew on Hispaniola, across northern South America and up to southern Mexico.

The holotype fossil was first studied by entomologist George Poinar Jr. of Oregon State University, and Alex Brown of Berkeley, California, with their 2012 type description of the new genus and species being published in the journal Systematic Parasitology.

The specific epithet stegosoma is coined from the Greek words stenos and soma meaning "narrow" and "body" respectively.

[1] Based on the flattened and rather flea like body plus inflated front femurs, simplified wing structure and location of origin, the genus was placed into the bat fly subfamily Nycterophiliinae.

The flattened body and front legs were likely used to burrow into the bat's fur to reach skin for feeding, as is done by modern Nycterophilia coxata.

No members of the subfamily are native to Hispaniola, which is depauperate of bat-flies, having two genera, Strebla and Tricholobius and five total species.