From Fensome et al., 2019:

Pithonella, Lorenz, 1902, p.46.
Emendations: Bignot and Lezaud, 1964, p.140; Villain, 1977, p.144; Masters and Scott, 1978, p.215; Keupp, 1987, p.39; Zügel, 1994, p.24. Calcareous ?dinoflagellate genus; for discussions on the affinity of this genus, see Streng et al. (2004, p.483), Elbrächter et al. (2008, p.1301) and below.
Taxonomic junior synonyms: Pirumella, by implication in Keupp (1981, p.44), who considered the "type species" of Pirumella, Pirumella edithvincentiae, to be a taxonomic junior synonym of Pithonella (now Pirumella) thayeri -- however, Lentin and Williams (1993, p.517) retained Pirumella; Palinosphaera, by implication in Zügel (1994, p.17), who transferred the type of that genus to Pithonella -- see under Palinosphaera for a full discussion; Cadosinella, according to Wendler et al. (2013, p.1098); Calcisphaerula, according to Villain (1977, p.144) and Wendler et al.
(2013, p.1098) (but see Elbrächter et al., 2008, p.1299); Andriella and Wallia, both according to Wendler et al. (2013, p.1098). Keupp in Keupp and Mutterlose (1984) included in Pithonella forms of unknown affinity only; forms which are demonstrably dinoflagellates were included in Obliquipithonella and Orthopithonella. However, Willems (1995a, p.61) considered Pithonella to represent calcareous dinoflagellate cysts. Wendler et al. (2013, p.1098) considered that Pithonella has probable affiliation with dinoflagellates, although they confusingly listed the
genus under both Calcitarcha (see Versteegh et al., 2009) and division Dinoflagellata; for the present we provisionally retain it as a dinoflagellate.
Type: Pithonella ovalis; holotype not designated.
Neotype: Wendler et al., 2013, fig.9, no.2; fig.17, designated by Wendler and Wendler in Wendler et al. (2013, p.1098,1104).