Adding the rattlesnake
Cortalus (Fig. 1), to the large reptile tree (LRT, 1226 taxa) nested it with Boa, the boa constrictor. A typical review of snake skull bones ensued, since it had been awhile since I looked at snakes.
Interestingly
some traditions (but not all, see Fig. 2) anchor the quadrate on a bone identified as the supratemporal (Fig. 3). Others label that bone a squamosal.
In the LRT
several snake-ancestor taxa, including Pontosaurus (Figs. 3, 4), show the squamosal (magenta) remains the quadrate anchor, as in all other tetrapods. The more medial supratemporals become vestiges and disappear in higher snakes.

Figure 1. Crotalus the timber rattlesnake in two views. The light blue dot is the last remains of the jugal.
So, is that anchor bone
the supratemporal? or is it the squamosal? Some authors label it one way (Figs. 2, 8). Others label it the other. The problem is, despite what other tetrapods do with that bone, it lies close to the parietal in snakes, like the supratemporal. Squamosals usually frame the upper temporal fenestra. Validated ancestral taxa with both bones provide the solution.

Figure 2. Is the anchor bone for the quadrate a supratemporal or squamosal? Some authors go one way. Others go the other (see figure 8). The LRT indicates the squamosal is correct. So do ontogenetic studies. See text for discussion.
Pontosaurus has both
bones (Fig. 4) and nests basal to snakes. Pontosaurus lesinensis (Gorjanovic-Kramberger 1892; Caldwell 2006) was a larger sister to Adriosaurus with a longer, deeper tail.

Figure 3. Pontosaurus skull in situ with relevant bones labeled. Note the squamosal leans into the parietal.
A reconstruction of Pontosaurus
(Fig. 4) clarifies the position and size of the squamosal, jugal, postorbital and supratemporal, matching those of other related taxa. Note the squamosals are pinched medially, the first step toward making those bones line against the cranium (parietal and other bones), as in snakes.

Figure 4. The skull of Pontosaurus reconstructed. Here the squamosal bends medially, reducing the size of the upper temporal fenestra, which is absent/confluent with the lateral temporal fenestra in living snakes. This taxon is basal to Tetrapodophis, Dinilysia and Pachyrhachis.
So where did the supratemporal identification come from?
I have not found the original source yet. Perhaps it came from the hypothesis that snakes are derived from mosasaurs (Fig. 6), but it is not easy to see how this happened.
The blogging professor, Darren Naish (1998-2009), wrote online here: Mosasauroids (mosasaurids and all of their close relatives) are platynotan lizards that, in the most recent analyses, share 40 shared derived characters with snakes (Ophidia) – therefore they share a single ancestor and form the clade Pythonomorpha Cope, 1869.”

Figure 5. Tylosaurus and other mosasaurs. Note the small supratemporal and large squamosal. Workers, like ED Cope and Darren Naish, found many similarities between mosasaurs and snakes, all by convergence according to other workers and the LRT.
According to Wikipedia
“Pythonomorpha was originally proposed by paleontologist ED Cope (1869) as a reptilian order comprising mosasaurs, which he believed to be close relatives of Ophidia (snakes). [However] Many recent authors demonstrate a closer relationship between mosasaurs and varanid lizards, like Varanus.” The latter relationship is supported by the LRT, which derives snakes from a long list of long-bodied taxa not related to mosasaurs and not tested by earlier workers, including tiny, four-legged Tetradophis (Fig. 6).

Figure 6. Snake skull evolution from Adriasaurus to the rattlesnake, Crotalus. Given the lack of a coronoid in Dinilysia and its presence in sister taxa makes me wonder if it has been displaced. The yellow bone, labeled the pterygoid, is a good candidate, but making judgements like that from a drawing is risky.
Pachyrhachis (Fig. 7) is a basal snake
with an expanded cranium, either reducing the twin posterior parietal processes or perhaps filling the space between them (because the cranium is relatively longer). Such a cranium appears to be inherited from tiny Tetrapodophis, which is preserved flat. In both taxa the squamosals lie upon the expanded cranium. The postorbital is fused to the postfrontal and no longer contacts the squamosal. The upper temporal fenestra is thus absent and/or confluent with the lateral temporal fenestra at the pre-snake/snake transition.

Figure 7. Pachyrhachis, a basal snake in which the postorbital no longer contacts the squamosal, which lies close to the parietal, losing the upper temporal fenestra.
Ontogeny
Werneburg and Sánchez-Villagra 2015 tested homology hypotheses by examining snake and lizard embryos then reported, “The ‘supratemporal’ of snakes could be homolog to squamosal of other squamates, which starts ossification early to become relatively large in snakes.” The authors wrongly reported, “We included for the first time Varanus, a critical taxon in phylogenetic context.” Varanus is not related to snakes in the LRT. The authors did not include Pontosaurus, Tetrapodophis and several other snake ancestors listed in the LRT. Without these taxa, the correct phylogenetic framework was not present in their study.

Figure 8. Snake skull form Andjelkovic et al. 2017 mislabeling the squamosal as a supratemporal.
Longtime readers may remember
I took a stab at this issue several years ago, but that was before the present tree topology of snake relations was established. Once I realized that I followed an invalid tradition back then, I trashed that post to avoid further confusion. I discover errors all the time, most often in my own work. I then repair those errors and misconceptions, which is the basis of good science, as everyone knows. Sadly, not every paleontologist follows this dictum.
On that note…
You might remember another traditional bone I-D mistake was also found in turtles,
in which the supratemporal was misidentified as the squamosal. So, yes, widespread misidentification can happen, and a wide gamut phylogenetic analysis illuminates such problems. So, bottom line, once again taxon exclusion is the single source of this long-standing problem.
References
Caldwell MW 2006. A new species of Pontosaurus (Squamata, Pythonomorpha) from the Upper Cretaceous of Lebanon and a phylogenetic analysis of Pythonomorpha. Memorie della Società Italiana di Scienze Naturali e del Museo Civico di Storia Naturale di Milano 34: 1–42.
Cope ED 1869. On the reptilian orders Pythonomorpha and Streptosauria. Proceedings of the Boston Society of Natural History 12:250–266.
Gorjanovic-Kramberge D 1892. O fosilnih cetaceih hrvatske i kranjske. Rad. Jugoslavenske Akademije Znanosti i Umjetnosti 111:1-21.
Linnaeus C 1758. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio decima, reformata.
Werneburg I and Sánchez-Vilagra MR 2015. Skeletal heterochrony is associated with the anatomical specializations of snakes among squamate reptiles. Evolution 69(1):254-63. doi: 10.1111/evo.12559. Epub 2014 Dec 17.
wiki/Crotalus
wiki/Boa_constrictor
wiki/Pontosaurus
wiki/Pythonomorpha