Help, new battery... Smoking alternator

If you are sure the polarity was correct while installing the new battery, then something has been going wrong with the alternator for some time. It probably killed the battery you replaced. So the brand new battery had enough power to burn up whatever was going wrong in the alternator (bad diodes). Okay. Disconnect the heavy red wire from the alternator and insulate it with lots of tape. Hook up the new battery. It will have enough reserve power to get you around to have the alternator tested and replaced. You could drive it around like that for a short while but eventually the battery will need a recharge/new alternator.

Somehow the polarity of the battery got reversed causing the spark and the smoke. Water under the bridge as to how. Do you know that car batteries can be charged backwards? It's rare but it can happen. At any rate right now you need to get on the road. Replace the battery, check the battery wire going to the alternator, after that run the car and see if the alternator will cary all the electrical loads if not replace the alternator if it checks good drive on, I used to be an electrical rebuilder and I've seen some ot these components run red hot and smoke but after cooling off they functioned just fine. I hope this helps take care