Unique Resource Marksman?
They mentioned the idea of energy for an ADC in their monthly Q&A, but said it was less feasible due to the marksman potentially becoming too oppressive.
Why not give them something similar to a Rage meter instead? Literally a resource that charges with auto attacks. There's a lot you could do with it.
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The amount of charge you gain from minions could be consistent and small to match the general harass potential of other ADCs.
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The amount you gain hitting a champion could be based on your distance from them. This would be pretty unique to a marksman. Stay far away and you get more access to your kit.
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Base your escape ability's cooldown or effectiveness on your current Rage when it is cast. This would mean if a melee champion gets to you before you build up your resource the cooldown or effectiveness of your escape suffers, allowing them to capitalise on catching you out. However, if you get the resource you need it becomes harder for them to lock you down, making your early fight pretty important.
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By default the abilities can be designed to be more effective mid-fight due to their likely lack of presence at the start of a fight. This means they could specifically have abilities for following up and it would work pretty thematically.