I think you are mistaken. All specialists provide the same yields, scaling with some techs. There are some buildings (walls of babylon), policies (industry finisher and others) and beliefs (mastery) that further provide additional yields, but again they are the same in all cities.
Where confusion may stem from is tradition gives buildings that have additional yields. Specialists building panel shows all the yields buildings gives (well, not all, but some). So terrace gardens show additional food, forge show additional science (but not additional production from arena). Of course, you get them from building, not from specialist. When you put a specialist, yield will adjust for it.