Summary for those in a hurry:
Specimens nesting at the base of the marine and terrestrial younginiforms need a good review, as in a doctoral dissertation. Many of the specimens below have not been described and the collection has not been tested in a phylogenetic analysis, except here in the LRT. And let’s not forget headless Galesphyris (Fig. 4), the last common ancestor of this monophyletic clade of (at present) wastebasket “young-” younginids (Youngina, Youngolepis and Youngoides) needs to be part of the picture. The Late Carboniferous diapsid, Spinoaequalis (Fig. 2), is the outgroup taxon in the LRT.
A new ‘Youngina’ specimen came to my attention
(Fig. 1) published in Sues 2019. Unfortunately no museum number was provided. Pending acquisition of that number, the new specimen was added to the large reptile tree (LRT, 1694+ taxa) just to see where the new one would nest among the many Youngina, Youngoides and Youngolepis specimens (Figs. 2, 3) already in the LRT. Scale bars indicate it’s a big one.

Figure 1. Unidentified specimen attributed by Sues 2019 to Youngina capensis. Here it nests to scale with the much smaller BPI 375 specimen basal to protosaurs, like the AMNH 9520 specimen assigned to Prolacerta.
Relatively few workers
have published on the Youngina, Younginoides and Youngolepis specimens. That is unexpected considering the key position in the LRT of these largely ignored taxa at the bases of several major clades.

Figure 2. Terrestrial Yonginiformes + Galesphyrus representing the marine clade, all to scale except the toned area containing protorosaurs, which have their own scale.
One traditional Youngina specimen,
short-legged BPI 3859, does not nest with the terrestrial taxa in the LRT, despite the many similarities.

Figure 3. The odd one out, the BPI 3859 specimen assigned to Youngina does not nest with the others, but with marine taxa.
However,
if headless Galesphyris turns out to be a junior synonym of Youngina, then the genus would be monophyletic across tested taxa. Let’s leave open that possibility. Otherwise, let’s rename them all appropriately.

Figure 4. If Galesphyrus was Youngina, the genus would be monophyletic.
At nine cm in length, the skull of the new specimen
is the largest skull assigned to the genus Youngina. Like the smaller BPI 375 specimen, it nests basal to protorosaurs in the LRT. Other specimens nest basal to Archosauriformes. As noted above, the BPI 3859 specimen nests basal to Claudiosaurus in the LRT along with other marine younginiformes, including plesiosaurs, mesosaurs and ichthyosaurs.
References
Broom R 1914. A new thecodont reptile. Proceedings of the Zoological Society of London, 1914:1072-1077.
Broom R and Robinson JT 1948. Some new fossil reptiles from the Karroo beds of South Africa: Proceedings of the Zoological Society of London, series B, v. 118, p. 392-407.
Gardner NM, Holliday CM and O’Keefe FR 2010. The braincase of Youngina capensis (Reptilia, Diapsida): New insights from high-resolution CT scanning of the holotype. Paleonotologica Electronica 13(3).
Gow CE 1975. The morphology and relationships of Youngina capensis Broom and Prolacerta broomi Parrington. Palaeontologia Africana, 18:89-131.
Olson EC 1936. Notes on the skull of Youngina capensis Broom. Journal of Geology, 44 (4): 523-533.
Olson EC and Broom R 1937. New genera and species of tetrapods from the Karroo Beds of South Africa. Journal of Paleontology 11(7):613-619.
Smith, RMH and Evans SE 1996. New material of Youngina: evidence of juvenile aggregation in Permian diapsid reptiles. Palaeontology, 39 (2):289–303.
Sues HD 2019. The Rise of Reptiles: 320 Million Years of Evolution.
Johns Hopkins University Press, Baltimore. xiii + 385 p.; ill.; index.
ISBN: 9781421428673 (hc); 9781421428680 (eb).