Your alternator may be smoking due to failure or a blown fuse.
First off, get your alternator fixed as soon as possible. Smoke coming from under the hood should always be taken seriously.
The bearing within the alternator can smoke due to excess friction when the alternator is dying. You’ll need to get it replaced.
Alternatively, the smoke may be due to a blown fuse on the alternator. This is good news, because the alternator is likely still usable. You should still get your car looked at to ensure everything is alright.