No sure I follow the question, but Specialty Cities produce a particular specified unit type type of city faster, and others less than normal. The actual speed depends on the "Efficiency" of the city. So to get the specialty bonus that city must produce. Be aware that capturing a city also reduces the efficiency by 10%. The city not producing anything is how it regains efficiency.
I'm asking if a Specialty City, when I capture it, can be made able to produce the very same units produced by the enemy , using the enemy's former plants and equipment located there-- because of strategic bombing to preserve infrastructure! This provides a real incentive to capture certain cities over others! I guess I'm asking if there's a legacy value to capturing a Specialty City. A legacy game somehow informs current play with previous play history. Providing the concept of a Speciality City, you've already laid pipe for it, so it came to mind. All existing Efficiency rules can apply, even reduced efficiency of 10%, but perhaps restoring production of a unit the city was known for should provide a faster than usual ramp up in efficiency which makes such captures a real lure, not to mention a mine field and patrols for protection.
ah I see - There's no history of production when capturing a city. When you take a city, you review the production, but it is reset to nothing and you make adjustments from there. There's no bonus for producing what was produced before. So you don't get to piggy back on production time already spent. But if a city is marked as a specialty for a certain unit type, that specialty is not lost on capture. So you would still get the percentage advantage/disadvantage depending on what you decide to produce there.