When the Cantus Firmus is in the 1st or 2nd voice, the bass is suppose to play the 5th note of the mode in the 2nd last bar. In the case of E Phrygian, the 5th degree is B which has however a diminished 5th (F natural) so what cadence should happen in the bar when in 3rd species?
Let's back up by thinking about this cadence in two parts first.
The CF will always end F-E. Your other voice will end D-E, with a suspension if possible (shown above).
Life gets tricky with a third voice because, as you mentioned, there is no perfect fifth below that F.
If your CF is in the top voice, you could try putting your suspension in the bass voice. Your middle voice would have to be consonant with D and F. A is your only choice. That A cannot go up to B for the last chord because it would form a parallel fifth with the bass. It descends to G# instead. You could also try putting your suspended voice in the middle, but this won't work. There is no way to give your bass a note that works in both measures without creating a bad parallel.
You'll face the same problem if your CF is in the middle voice. Your top voice can be A-G# and your bass suspended. But if you put your suspension I. The top voice nothing will work in the bass.
If your CF is in the bass, your upper two voices have more options:
The extra voice might even be able to go up to B, if that forms a fourth with the voice rising to E instead of a fifth.
The true difficulty in this mode is that the final two chords are separated by a second (D to E) and not a fourth like most other modes (A to D in Dorian, for example). That means there are no common tones between the two chords.
Phrygian mode in practice has several distinctive cadence available, as taken from "Sixteenth-Century Polyphony: A Basis for the Study of Counterpoint" by Arthur Tillman Merrit, p.93, example 147. The penultimate chord is "often" in first inversion, and the F is never sharp. These could be adapted as need be for the quarter notes of the 3rd species. These also may not be suitable if your exercises mandate a different style of counterpoint.
There is also the plagal cadence, but that will not fit this particular counterpoint exercise (A-C-A-E going to a E-B-G#-E) and might get you negative points on a scholastic counterpoint exercise due to the bass and tenor voice motion, but that's what the book shows. It may be better to study various exant works in the phyrigian mode (the Bach chorales, or older vocal works) to see how the cadence is handled without the textbook distillation.