Note added August 1, 2019:
I wonder if the prickly elevated fore fins of Iniopteryx and kin were an early attempt at hitchhiking, convergent with living remoras? Reduced dorsal fins make that possible.
Distinct from all other tested taxa,
Iniopteryx (Fig. 1) and kin extend their pectoral fins from the dorsal region where they ceased working as fins and began working as fancy secondary sexual traits (Fig. 2). This is similar, but different than a sister chimaera, Falcatus (Fig. 3), famous for its lone long horn.

Figure 1. Figure 1. Skull of Iniopteryx in situ from Zangrel and Case 1973 (above) and reconstructed (below) using DGS techniques.
Zangrel and Case 1973
introduced us to a new clade of ratfish the named the Iniopterygia (= Iniopterygiformes). All four had a similar body plan, differing mainly in the decorations. Wikipedia reports, “The closest modern-day relatives of the Iniopterygii are the Chimaeras (Chimaeriformes).” In the large reptile tree (LRT, 1505 taxa) Iniopteryx nests within the Chimaeriformes, not as a sister taxon.
Evidently no one yet
has traced the skull bones of these crushed Late Carboniferous taxa, except as broad skull outlines (Fig. 2). Here (Fig. 1) that problem is resolved.

Figure 2. The Iniopterygidae include Iniopteryx, Promexyele, Iniopera and Sibyrhynchus. These reconstructions are from Zangerl and Case 1973 and the captions label them “tentative.” Note that none of the skulls include details.
A sister in the LRT
is Falcatus (Fig. 3), which also has a dorsal secondary sexual trait and a skull morphology similar to that in Iniopteryx. Normal pectoral fins emerging from the chest area are present in Falcatus and all other vertebrates with fins/limbs.

Figure 3. Falcatus skull. This taxon is close to Polyodon in the LRT.
Chimaera are bottom dwellers,
and sometimes ‘the bottoms’ are very deep. Their eyes are large to pick up the rare photons that make it to those inky depths from above, or are produced by self-illuminated benthic organisms.

Figure 4. Subset of the LRT focusing on basal chordates, vertebrates and bony fish not related to tetrapods. Scomber and Istiophorus are new additions to the gold clade.
References
Zangerl R and Case GR 1973. Iniopterygia : a new order of Chondrichthyan fishes from the Pennsylvanian of North America. University of Illinois Urbana-Champaign. Chicago : Field Museum of Natural History.