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Fighters are classed as vessel massing 500t or less. While they are designed as normal ships they are built via the industry screen, not in shipyards. Built fighters operate and serviced on motherships, and can be organized into squadrons for ease of use.
Designing a fighter
Fighters are considered Fast Attack Craft and do not require a bridge, they can also use special "fighter only" components. Currently the only component that can be set as such is Beam Fire Control, which gains a bonus to tracking speed of beam weaponry.
Due to the size limitation, Fighters are typically designed as fast, short-range craft that don't spend a of time outside their hangars. As such they require minimal deployment time and maintenance supplies. Fighter engines are optimized for extremely high speed with low fuel efficiency. Succinctly, any engine can be used on a fighter provided the fighter's overall tonnage does not exceed 10 (HS). To keep fighter weights down, you should invest in smaller Crew Quarters, Engineering Sections and Fuel Storage.
Gauss cannons make the best point defense fighters, but without skilled officers inaccuracy with small GCs is a problem. Reduced size lasers pack the best punch, but turreting them is prohibitive. Missiles are the most flexible in terms of fighter size and role, fighters are often equipped with Box Launchers to maximize their hitting power, but these require a greater logistical effort.
You might also think about omitting Engineering Spaces, as fighters usually don't spend a of time outside their hangars.
Building and Maintenance
Fighters can be fabricated on a colony with Fighter Factories, a type of installation. From the Industry tab F2 there is a pull-down menu called Construction Options. Select Fighters. A list of all your fighter designs will appear. Select one, and just like ordinary construction, place a number and a percentage. Unlike ordinary construction, you also have to give define a task group for the new production. It is important that you do this, as any fighters made without a task group designation will be lost.
Fighters operate from motherships. These might be huge Carrier leviathans, small cruisers or even Planetary Defence Centres. Any class with a hangar decks, boat bays or both, with enough space as a valid mothership. These provide a capability to house fighters, provide repair, refuel, and rearm. Remember fighters are not serviced by maintenance facilities nor can be refitted.
Once fighters are built, they can be organized into a squadron via the Fighter Squadrons Window F7 for ease of use. Once there select the 'Reorganize Squadron's' tab. Your new fighter will appear here. Click on the 'New' button at the bottom left. This will create a new squadron. Then simply click on the fighter under 'no assignment', and click on the left arrow to move it to the squadron.
Now the squadron has a fighter, but the squadron itself needs a home. Open up the motherships' dropdown and select a home for the squadron, click on the squadron and then on the assign button. The fighter, and its squadron have been assigned a base.
All that is left is to 'Recover' the squadron to place them safely in their hanger or boat bay. It is advisable to keep them in a hanger or boat bay as the maintenance clock is off while they are stored.