I regularly run an Adventurers League table at a local game cafe. For the last few weeks I've been trying to incorporate a college age player into the group who hasn't worked out at other tables.

He's been displaying some disruptive behavior like drawn-out fights over rulings, fudging stats, and getting frustrated when I point out mistakes in his use of features. Rude and sudden outbursts--although enthusiastic ones--have already deterred several new players from returning to the store. He's gotten slightly better, but the same exact mistakes occur session after session. 

When I approached him one-on-one before a session to figure out how we can work together better, he became slightly irritated and claimed that he's forgetting things as a result of his ADHD and that there's nothing he can do about it. He used a similar explanation later when I pointed out that this was the fourth time I had to repeat a specific setting description to him while he was on his phone.

I think he feels targeted due to his ADHD, after he has claimed I'm being unfair with rulings and challenges, especially when faced with scenarios that make it difficult for his monk to simply walk up and punch enemies.

I want to work with this player if possible. Since I have no perspective on ADHD I'm blind to how much of this is justified, but I'd be loath to let him push players around at my table. How can I effectively address this player's behavior in a way that won't close him off further?

What measures can I take to make this player feel welcome at my table without allow his distractions to disrupt the existing group, or letting him get away with being overly aggressive? Since this is Adventurers League, I don't really have a way to approach him in private, but I could try talking to him before the session again. But at what point can I safely say it's just not going to work and he's going to keep on fighting the other players/myself?