Among the oddest fish in the late Paleozoic seas,
are relatives of Helicoprion, famous for its buzz saw teeth (Fig. 3) that grew in a single spiral set in the mid-line of the jaws. Unfortunately not enough is known of the skull to attempt a nesting in the large reptile tree (LRT, 1812+ taxa) at present.
Earlier
Harpagofututor (Figs. 2, 3), a Carboniferous relative of today’s moray eel (Gymnothorax), was tentatively allied with the buzz-saw clade because it shared a small medial tooth row.
Today
Edestus heinrichi (Leidy 1856; Fig. 1; FMNH PF2204; 25cm skull length; Pennsylvanian) joins this clade with its scissors-like medial jaws (Fig. 1) and enough skull to work with.
From the Tapanila et al. 2020 abstract
“Sharks of Late Paleozoic oceans evolved unique dentitions for catching and eating soft bodied prey. A diverse but poorly preserved clade, edestoids are noted for developing biting teeth at the midline of their jaws. Helicoprion has a continuously growing root to accommodate >100 crowns that spiraled on top of one another to form a symphyseal whorl supported and laterally braced within the lower jaw. Reconstruction of jaw mechanics shows that individual serrated crowns grasped, sliced, and pulled prey items into the esophagus.”

From the abstract, continued.
“A new description and interpretation of Edestus provides insight into the anatomy and functional morphology of another specialized edestoid. Edestus has opposing curved blades of teeth that are segmented and shed with growth of the animal. Set on a long jaw the lower blade closes with a posterior motion, effectively slicing prey across multiple opposing serrated crowns.

Tradtionally
Edestus and Helicoprion are portrayed with a shark-like body, but phylogenetic bracketing gives it a moray eel-type body (Fig. 5), like Harpagofututor.

From the abstract, continued:
“The symphyseal dentition in edestoids is associated with a rigid jaw suspension and may have arisen in response to an increase in pelagic cephalopod prey during the Late Paleozoic.”
Note that Gymnothorax, the extant moray eel (Fig. 6), also has large palatal teeth along the symphysis (= midline) by homology.


Pulling prey deeper into the jaws
is a trait shared with the moray eel (Gymnothorax, Fig. 6), though done with an extra set of esophageal jaws (Fig. 7), distinct from the buzz-saw and scissors sharks.

Special thanks to reader JeholornisPrima
who sent a link to the Tapanila et al. 2020 paper on Edestus this morning to get this ball rolling.
References
Leidy J 1856. Indications of five species, with two new genera, of extinct fishes. Proc Acad Nat Sci Philadelphia 7:414.
Tapanila L, Priuitt J, Wilga CD and Pradel A 2020. Saws, Scissors, and Sharks: Late Paleozoic Experimentation with Symphyseal Dentition. The Anatomical Record 303:363–376. https://doi.org/10.1002/ar.24046
Glad to have helped! Certainly interesting (and unexpected) to see Edestus nesting with Harpagofutator. Still, that’s the whole point of the LRT.
Correction: HarpagofutUtor!