I imagine that it might be pronounced:
kye EE suh
kah EE suh
Which is it? Or perhaps there is no established way and one shouldn't care too much.
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I think that your best bet is probably option 2: "kah EE suh" (similar to the pronunciation of "naïve"). The phonemes match the spelling correctly (particularly the umlauted ï in "Caïssa" [ref. 1]), and it fits with the tonal stressing of multiple Thracian-related [ref. 2] languages.
Historically, both Greek and and Turkish (largely Hittite and Assyrian influences, in Thracian times [ref.s 3 & 4]) would appear to have likely had the strongest early influences.
Satemization of the Thracian language [ref. 5] would indicate the initial “C” to typically be an “s” sound, though it seems that in the case of “Caïssa” it was more likely a “k” sound.
Given the remnants of the Thracian language available to us [ref. 6], there seem to be insufficient data to ensure “correct” pronunciation. Thracian words seem [to me] to be equally likely to be most closely related to Latin, Greek, and several Balto-Slavic languages.
If Gottfried Schramm's derivation [ref. 7] is correct, then his Bessian-Albanian link would indicate that the “i” is indeed a “long e” (ï) sound [ref. 8].
How To Pronounce Caissa Please listen to all the options to get a sense on how to pronounce casissa.