Hello, the German word Jäger (or Jaeger) in German means Hunter. So it is very possible that Jaeger became Hunter.
If your ancestor was German-born and emigrated, his LNAB was most likely Jäger or Jaeger.
The spelling with Y (Yager, Yaeger) would be American. The letter Y would not be used at the beginning of a word in German.
I and J were equivalent in Latin. So Iaeger is a equivalent, obsolete spelling of Jaeger/Jäger.
In short, I would use Jaeger (or possibly Jäger) as LNAB. It would be nice if someone more experienced with this point weighed in, though.
Good luck with growing your tree!