Offensive beam fighters have a huge handicap to overcome in Aurora, they have to be able to survive offensive and defensive fire to reach the short ranges dectated by the limited size of the weapsons they can carry.
The maximum size for a fighter is 10 hull spaces. This is a limitation for fighter factory production, anything larger requires a shipyard slip.
Fighter engines are 1hs and your limited to only 1.
The smallest beam weapon, that is not reduced size, is 3hs. Plus you need a powerplant, figure between .5hs to 2hs for this depending on capacitor in the beam and the cyclic rate you want.
Your also need a beam fire control, at least 1 command module, and some fuel.
At this point the fighter is someplace north of 6hs with less than 20% hs in engine and this leads to fighters that are bearly faster than ships with 25%hs in engine even though fighter engines produce 3x more power per hs than miltary ship engines. Yes, reduced size lasers exist in the game, but the recharge penalty means that thier effectiveness is greatly reduced.
Gauss Cannon have been mentioned. They're extremely short range when compared to all other beam weapons and twice as massive. The reduced size versions sacrifice accuracy to the point near uselessness.
The only offset to these handicaps is swarms of hundreds of beam fighters. You have to provide more targets for the OPFOR to eliminate than they have to ability to deal with. This presents it's own problem, hanger space so that the maintenance clock doesn't kill them. For a planetary defense this can work, but offensively is segnificantly larger problem.
Strategicly and Logisticly, beam fighters are a losing proposity in Aurora.