Since aviation fuel contains no water...
However... combustion of hydrocarbons tends to produce things like water and CO2 (the tailpipe on my truck was drip...drip...dripping water just after I started it up this morning. As I recall, it was doing that because water was being produced by the combustion of gasoline, and that water condensed in my cold exhaust pipe...).
Leaving the rest to those of you who live this stuff or have more time than I right now to find the details!
Dave
Edited to note that there is always the possiblity that jet engines do NOT produce water vapor, but rather, well, you know...