Updated December 15, 2020
after many more taxa have been added to the clade of basal gnathostomes (see below)..
Not many fossils are fossilized while mating or courting.
And not many have an ‘antler’. Today’s ‘antler’ (Figs. 1-3) is found on Falcatus, an extinct ratfish, according to both traditional studies and the large reptile tree (LRT, 1495 taxa).

Figure 1. Like pulling the bedsheets off of spooning honeymooners, this mating pair of Falcatus were caught in the act of courtship. That’s the female biting the males antler. He is identified by his pelvic claspers. Female: MV 5386 above. Male: MV 5385 below.
Distinct from Chimaera
Falcatus has a jaw joint far behind the orbit, as in sharks, not below the orbit as in Chimaera (Fig. 4). Falcatus also has a shark-like tail fin, not the long straight streamer found in Chimaera.

Figure 2. Falcatus skull. This taxon is close to Polyodon in the LRT.
Lund 1985 considered Falcatus
to be a member of the clade Cladodontida (later a junior synonym of Symmoriida) and a member of the family Stethacanthidae. Here with far fewer tested taxa Falcatus nests with Chimaera, the ratfish (Fig. 4).

Figure 3. Falcatus traced with DGS methods with reconstructed freehand image applied from Lund 1985 based on CM37532b and caudal outline from CM 35471.
Several hundred million years have passed
since Falcatus in the Mississippian (Early Carboniferous) to the present day, plenty of time for the propulsion system to shift from the tail to the pectoral fins.

Figure 4. Chimaera monstrosa in vivo.

Figure y. Basal Gnathostomata with the addition of Rhinochimaera.

Figure 5. Shark skull evolution according to the LRT. Compare to figure 1.
References
Lund R 1985. The morphology of Falcatus falcatus (St. John and Worthen) a Mississippian stethacanthid chondrichthyan from the Bear Gulch limestone of Montana. Journal of Vertebrate Paleontology 5:1–19.
St. John OH and Worthen AH 1883. Description of fossil fishes: a partial revision of tehe Cochliodonts and Pasmmodonts. Geological Survey of Illiniois 7:55–264.