It is a romance based conlang which refers to itself as "cagieje" because it is spoken in the city and district of "Ea Cagia" which literally means "the homeland". It is the daughter language of the Castelese language spoken in "Castelstad", with which it is still mutually intelligible.

I need a name for "cagieje" that can be used in English, I tried "Cagian" but that sounds too much like "Cajun". Any ideas?

It is pronounced /kaʝˈɛʒɛ/

Cayese/Caïese?

The triphthong is a bit hard to pronounce :/ I assume that is pronounced /kɛjˈiz/ or /kajˈiz/ ?

It's not a triphthong IMD. The spelling with the diaeresis is just an attempt to force the pronunciation /kaɪ̯ˈiːz/ since the element cay would normally suggest /keː/.

It's a good suggestion, I'll try it.
I've thought of names for it in other languages: Kägisch /ˈkegɪʃ/ (German); Cageais /kaˈʒɛ/ (French); Callés /kaʎˈes/ or /kaʝˈes/, or Cagiés /kaxˈjes/ (Spanish)

How about Cagyese, with similar pronunciation to linguoboy's suggestion - the 'gy' more representing a stronger 'y' or 'i'???

I don't think a single monolingual English speaker would get that right. Everyone would pronounce the g (either as /g/ or /ʤ/) and most would make the word trisyllabic.

Is this place in a cold climate? If so, I've always loved the ending acian, or lacian. It reminds me of the word glacier.

You could do- Caglacian, Calacian, Caylacian, Cacian.
Try looking through lists of language names, and add the ends on to your name. You'll come up with something sooner or later.

-Connor