1994 Corsica smoking near alternator what could it be

Could be alternator belt slipping,or may be oil leaking from valve cover.

If it is coming from the alternator itself, you may have a frozen bearing and it either needs replacement or a new alternator. Is there oil dripping on the exhaust manifold? A gasket leaking oil may be the problem. If your engine is fairly clean, use a paper towel and see if there is fresh wet oil in the area of the smoke that may be dripping onto the manifold. If the belt was slipping, you'd hear the belt squeal, or the pulley on the alternator is not moving,