Hmm, Sorry. Just trying to help
I had one in 5 gal hex for several years, never got more than about 2-3 inches. I know they can live several years at this size, but not to their full potential and lifespan i'm sure, so Ideally, its probably not the best for a smaller tank long term. (although I know they're pretty good starter fish) They could live in that aquarium for a few years ( by itself ), especially if you had planned to get a larger or transfer to a pond. So technically you could, but as with any fish in this hobby, research is a must before, to see what works best for you. Each fish / experience is different.
Im not trying to make this a goldfish topic though. I certainly dont know everything about fish for sure, and im constantly learning, but just offering suggestions from what i've had luck with and experience with
Anyway, back to answering the original question.. theres a few small species that would work well in a 15 gal. maybe one or two of the following: Gobies, blennies, clowns ( common or percula ) royal gamma, firefish, etc.
Make sure to keep a good eye on your water parameters as they can fluctuate quickly in a small tank.
good luck