If you want fighters in a game, the question that needs to be answered is WHY?
What can fighters do that the run of the mill starship can't?
In modern day combat, fighters can extend a ship's reach deep into land. Sure, cruise missiles can also do this, but fighters have a great degree of flexibility, whereas a cruise missile is single minded once it is launched.
To extend this analogy to GalCiv, perhaps fighters can assist in ground assaults as well as in space combat?
What else could fighters do, that makes them unique and able to fulfill specific functions that starships can't?
My experience so far with Gal Civ III is that bigger is better, due to logistics limitations. Perhaps fighters don't count against logistics caps? Do they provide a comparable amount of firepower, etc. versus the system slots they replace? What makes a fighter better than just another laser cannon?
Perhaps fighters make excellent scouting platforms, so ships that carry fighter squadrons can increase their sensor range (combat space patrols).
Perhaps fighters can perform 'long range strikes' versus ships in an adjacent square/hex, thus increasing the 'reaction range' of ships and starbases. Sure, the fighters will be on their own (no big guns to back them up), but depending on how powerful their weapons are they can still cripple/destroy targets that have weak enough defenses for the fighters to contend with.
If 'Stealth' designs were introduced into GalCiv, where you have to be MUCH closer to a ship before you see it on the galactic map, perhaps fighters on CSPs will spot a stealth design a little further away than just a ship on it's own.
In modern day combat, offense is much more powerful than defense. This is why one lone F-18 with shipkiller missiles can threaten a squadron of enemy ships, and stand a good chance of sinking one or more of them. Hence, why aircraft are so important in the current military regime. Ships have their own roles to fulfill, of course - fighters aren't very good at transporting a division of troops. Sure, transport aircraft can do this, but transport ships can carry a good amount of armor, supplies and such, at a cheaper cost.
BTW, I would not be very supportive of the current state of military affairs in GalCiv. Ships should be powerful, fighters not so much. Fighters, if introduced, should augment ships in combat, not overshadow them.
So again, if fighters are introduced, which would be easy to do, they need to fulfill roles that they are uniquely suited for, that ships aren't doing already.