Which ranged champion has the highest attack damage wave clear potential in League of Legends?
There isn't really a "best" marksman to farm with. Almost all ranged AD champions have the advantage of getting easy last hits due to the fact that they build AD and have basically unlimited resources due to the fact that they don't spend any mana on their "main attack", however there are some that have certain advantages.
Since there are usually two people (Marksman and support) on bot there are certain situations where different champions excel at farming while others are struggling. Therefore I will look at two main aspects of farming: The ability to farm minions and the safety while doing so.
In general there are a few things that contribute to the ability of a marksman to farm well. These are:
Attack speed buffs
These help in pretty much every situation. It just makes it plain easier to last hit and leaves more room for error since you might be able to add in a second hit if you screwed up your last.
Notable examples are Jinx, Varus and Ezreal
High range makes it extremely safe to last hit and it allows for easy switching between harrassing and farming.
Notable examples are Jinx, Caitlyn and Ashe
Area of effect spells/Attacks
This makes waveclearing a lot easier and especially midgame you can kill multiple minions with a single use of an AoE spell.
Notable examples are Jinx, Sivir and Varus
Auto attack resets/Spammable abilities
Auto attack resets or spammable abilities are similar to an increased attack speed. They allow for more errors and can be used to quickly lasthit something.
Notable examples are Ezreal, Sivir and Vayne
Last but not least we have gapclosers. This is again something that doesn't directly affect farming, however if you have the extra safety of a gapcloser you can usually go in for more risky creeps without getting punished too hard by the enemies.
Notable examples are Ezreal, Sivir and Kalista
Based on the factors above it's possible to narrow down the "best" farmers. Obviously these champions will perform differently based on mastery of the champion and the situation they're in but it's pretty safe to say that the following champions are extremely strong, safe or both while farming on bottom.
Probably one of the strongest. She has AOE, high range, low mana cost, attack speed steroids and minor defensive spells. Her only real disatvantage is the fact that she doesn't have any gapclosers.
Sivir has extremely strong waveclear while also staying relatively safe with her spellshield. She also has an auto attack reset and an attack speed buff past lvl 6. Her disadvantage is her low range and lack of gapclosers.
For people who are familiar with lasthitting as an ADC this will probably be the safest of all. You have a free flash every 6-10 seconds and a spammable Q plus an attack speed passive. The only disadvantage there is is the high skill cap of the champion.
She's kind of like a mix between Ezreal and Jinx. While she doesn't have the mobility of ezreal or the damage of Jinx she has a mix of both that make her safe and strong while farming.
As I said. There is no real best champion but most mentioned above will outperform players on the same skill level that aren't playing those champs.
There are several ADCs that specialize in clearing waves quickly.
Sivir is probably the queen of wave clear when it comes to ADCs. Her Q does a lot of damage after it's been leveled a few times, plus her W will hit every single minion in a wave and can also crit (in fact, if a W-empowered auto attack crits the first target, all subsequent targets will also be crit). I have cleared 12-15 minions in about 2-3 seconds come late game with Sivir's strong AoE abilities.
Jinx is also very good at clearing waves quickly thanks to her rocket launcher, which deals splash damage to any units near your target. Similar to Sivir's W, if Jinx crits on her primary target, the splash damage will also crit. Runaan's Hurricane is especially strong on her, since the extra bolts that the item creates will also deal splash damage. It's very possible to clear an entire wave of minions in one or two auto attacks with Jinx.
Graves is a short-range AoE ADC, so it should come as no surprise that he is also decent at clearing waves. His Q, when properly placed, can deal a lot of damage to minions, plus his auto attacks on their own can hit multiple minions at once. His auto attacks also push non-champions/non-epic monsters back, which prevents them from attacking him if they are melee.
Lucian is very good at clearing waves because his primary damaging ability (his Q) travels through minions and does damage to anything in its path. Combined with enough cooldown reduction and his passive, he can dash around and clear a wave of minions pretty quickly. Additionally, his ult does a lot of bonus damage to minions, so it can also be good for waveclear in some situations.
Tristana can be okay for wave clear due to her passive, which deals a little bonus damage to any enemy units close to a unit she just killed. Additionally, her E also does a significant amount of damage in a small blast radius if fully charged. However, it has a moderately long cooldown, so she's not as good as the other champions I've listed here when it comes to waveclear.
Finally, buying Runaan's Hurricane on any ADC will give them significantly more wave-clearing power, since they will deal damage to more targets per auto attack. On some champions, this item is very important - after purchase, Twitch's waveclear strength goes up quite a bit since each bolt applies a stack of his passive, which in turn boosts his E ability damage. It's a similar scenario when buying the item on Varus. However, Runaan's might not be the best item to buy on every ADC. For example, though it would help Vayne clear waves much better, it's not as optimal as something like Phantom Dancer or Rapidfire Cannon since Vayne's specialty is dueling and teamfighting, not clearing waves.
As mentioned by others, Sivir, Caitlyn, Twitch, Jinx, Tristana, Lucian, Graves, and Ashe have good wave clear and their wave clear is generally amplified by Runaan's Huricane (doesn't help Sivir, Lucian, or Graves as much as the others), but they neglected to mention a few others who have good ranged attack damage wave clear.
Varus has exceptional wave clear having two abilities capable of dealing large amounts of damage to minions. If it is safe enough to auto attack a few times and you have Runaan's Hurricane, you can stack your W passive up on several minions and amplify the damage your Q or E will do to them and can usually clear a full minion wave with a few autos and a Q or E based on which you maxed first and what items you have. If you want to stay safe and clear from a far, you can use Q from max range to clear waves quite quickly from relative safety.
Corki is a somewhat unique pick as he does a lot of hybrid damage, but you mainly build ad on him, making him a ranged attack damage dealer who also deals a lot of magic damage. His Q and R are both high damage ranged AOE abilities and can be used to quickly clear waves along with his E ability which does AOE damage in a cone in front of Corki while it is active.
Jhin when using his abilities can clear waves quite quickly if he combos properly. If you use an E on the caster minions and then get a minion low enough with a few autos that your Q will kill the minion, it will deal significantly more damage on its bounces. This allows you kill minion waves fairly quickly, and your W can help as well as its damage will pass through to all minions in the line provided the shot is not blocked by a champion.
Jayce is both a melee and a ranged champion, and when in ranged form, he can use his Q to clear minion waves quickly with the AOE explosion around the target area. A properly aimed Q can hit multiple minions at a time, and if amplified with his E, can do considerable amounts of damage from a long range and clear minions quite quickly.
Quinn also has decent wave clear with her Q, as it has an AOE explosion and does quite good damage.
While not always used for wave clear, Miss Fortune, Jhin, Draven, and Twitch can use their ultimate abilities to clear a wave much faster than normal.
Besides these options for ranged champions with attack damage wave clear, many mages such as Ahri, Lux, Syndra, and Ziggs have excellent ranged magic damage wave clear.