Tripteroceroides is a pseudorthocerid

Pseudorthocerida

Pseudorthocerida are generally straight longiconic nautiloids with a subcentral to marginal cyrtochoanitic siphuncle composed of variably expanded segments which may contain internal deposits that may develop into a continuous parietal lining.. Cameral deposits are common and concentrated ventrally...

 from the Lower Carboniferous (Mississippian) belonging to the family Spyroceratidae

Spyroceratidae

Spyroceratidae are defined as Pseudorthocerida with uniformly slender siphuncle segments, longer than wide, that contract sharply near either end, in which endosiphuncular deposits first form a compete annulus before fusing ventrally....

 . Pseudorthocerids are nautiloid cephalopods with expanded siphuncle

Siphuncle

The siphuncle is a strand of tissue passing longitudinally through the shell of a cephalopod mollusk. Only cephalopods with chambered shells have siphuncles, such as the extinct ammonites and belemnites, and the living nautiluses, cuttlefish, and Spirula...

 segments included in the superorder Orthoceratoidea

Orthoceratoidea

The Orthoceratoidea is a superorder , sometimes considered an infraclass or even a subclass, that comprizes nautiloid orders that have orthoconic to slightly cyrtoconic shells and central to subcentral siphuncles in which there may be internal deposits...

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Tripteroceroides has a depressed, apically curved, straight shell with the under side (the venter) flatter than the upper (the dorsum). Sutures have slight lobes (to a rear inflections) as they cross the upper and lower sides, and saddles (diversions to the front) on either flank. The suture is subventral (near the lower side), with flared out necks and subcylindrical segments, sharply reduced in diameter at either end.

References

• Sweet, Walter C. 1964. Nautiloidea -Orthocerida. Treatise on Invertebrate Paleontology, Part K. Geological Soc. of America and Univ of Kansas press.
• Tripteroceroides-Paleodb