I’ve seen all three of the words Jagertee, Jägertee and Jagatee appear on various occasions, for instance on Wikipedia. It would appear that all three spellings are correct.
Are they indeed all correct? If so, is it the “official spelling” or are some only used in certain dialects or certain regions of German speaking countries?
All three spellings are routinely used. The "correct" spelling, of course, would be Jägertee (hunter's tea), but in my experience the other variants, particularly Jagertee [1] are actually more common. As is commonly the case with dialect expressions there is no fixed orthography, of course, hence the confusion.
With that in mind, EC Regulation No 110/2008, which protects certain geographical indications of spirit drinks, makes no difference and lists Jägertee/Jagertee/Jagatee as full synonyms. I think that's about as official an answer as we're likely to get in that case :) [2]
[1] The Austrian Dictionary (ÖWB) even lists Jagertee as ugs. = umgangssprachlich (colloquial)
[2] Interestingly enough, Hüttentee is now a protected German beverage. I never knew ...
The Standard German terms and spellings for ‘hunter’ and ‘tea’ are Jäger and Tee, so their compound would be written Jägertee ‘hunter’s tea’. (If the left-side component ends with -er there usually is no fuseme “Fugenlaut” like s or n, therefore it’s not ?Jägerstee.)
However, at least two types of words don’t necessarily have to follow basic graphotactic rules: proper names and words from other languages. The latter can be interpreted loosely, so also applies to German dialects and varieties, which usually have no conventional spelling rules. It is mostly reserved for nouns that refer to objects that are exemplary for the culture the dialect is spoken in. Therefore, we tolerate Dirndl, Wiesn and Mass in Standard German texts about the Oktoberfest etc., although the expected spellings would be Dirndel, Wiesen and Maß or at least Dirnd’l and Wies’n.
Jagertee and the even more peculiar Jagatee may qualify for both, proper name and dialectal spelling. If a name that makes it easier to legally protect by trademark laws, but it appears Austria succeeded in also claiming standard Jägertee for marketing of local products.
In conclusion, if you wanted to name some kind of hot beverage (not necessarily containing alcohol) that some hunters regularly drank, you could call it Jägertee, but if you are referring to the punch served at (not exclusively Austrian) après ski entertainment nightclubs (Hütten ‘shacks’) you may also use Jagertee or even Jagatee. They sound alike and different from Jägertee.
If there was a city or region called Jag or Jage, the tea special to that area would probably be called Jager Tee, by the way. Otherwise it’s always written as a single word as above – or at least with a hyphen if the left-hand word should be emphasized for some reason, e.g. for being a proper name as in Darjeeling-Tee or Ceylon-Tee.
