First things to check:
1. Belt is properly tightened and running OK. Bearing on alternator turning smooth.
2. Battery has been checked. Load tested to make sure it does not have internal problem.
3. Slo-blo fuse pulled and ohm'ed for continuity.
4. Good ground from alternator case to battery negative terminal. Connectors on alternator and corresponding cables bright, shiny, good electrical contact.
Let us know what you find and will go to next steps if needed. Where are you reasonably close to such as DFW, Austin, Houston, Midland, etc?