I recently had a new alternator put in my 1990.

I recently had a new alternator put in my 1990 plymouth acclaim, but because they no longer make the original part the mechanic had to put a different one in. Is this something that would cause problems with my car? Since the work has been done just over a month ago ive already shredded a brand new belt. I took it into bell tire and they tried replacing the belt but they said it was being shredded again and to take it to the dealership who said the part is wrong and I need a refurbished part which will cost me $700 on top of what I already paid for the new alternator.