Pethil in Hebrew. See note on Exodus 28:28. Some say that this was a twisted thread attached to holes in both ends of the plate to tie it to the head (Yad, Kley HaMikdash 9:3; Ramban). Others maintain that there was a third thread going through a hole in the middle of the plate and over the turban, and then tied to the other two threads in the back (Rashi; Raavad, on Yad. loc. cit.).
According to another opinion, the pethil here was a 1 1/2-2 inch band attached to the plate, going around the head (Chullin 138a, according to Rabbenu Chananel, Meiri, Shabbath 57b; Rif 26b; Arukh s.v. Kippah; cf. Genesis 38:18). Some say that this band was (also?) under the plate to protect the head from the hard metal (Rambam on Shabbath 6:1).
Others, however, say that the cap mentioned in the Talmud (Chullin 138a) was a blue cap that went over the turban (Josephus, Antiquities 3:7:6; Wars 5:5:7). See note on Exodus 28:39, 39:28.