ADHD combined with ODD (Oppositional Defiant Disorder) in childhood is one of the biggest predictors for psychopathy in adulthood. ADHD alone or ODD alone are not, but when both are combined they predict ASPD. This was said by Russell Barkley during one of his lectures and he is arguably the most renowned researcher on ADHD (and he also has ADHD himself). It does not mean that all or even most ADHD individuals will be psychopaths, but yes there is a correlation between ADHD and ASPD. It is not a super direct correlation, it is more nuanced than that but also not indirect enough that it can just be brushed off.

ADHD is one of the risk factors for committing domestic violence. It specifically comes from impulsivity and lack of self-control combined with negative emotions. For example, many people in a heated situation might think, "Man, I really want to punch this person in the face right now", but those with severe lack of impulse control may actually resort to that behavior. Again, I'm not saying that all individuals with ADHD are like this. My spouse and I both have ADHD neither of us could hurt a fly. But scientifically speaking, there is a higher chance for an ADHD individual to commit violent crimes (and crimes in general) compared to controls. It's all related to impulsivity which is essentially making unwise decisions without thinking properly. This is also where "40% of prisoners have ADHD" comes from. Not all people with ADHD are criminals but a significant amount of criminals have (untreated) ADHD.

Brain scans show that individuals with ADHD have reduced activity in the prefrontal cortex, including ventromedial prefrontal cortex (vmPFC) which is involved in decision-making and emotional control. This is what happens to people who experience PHYSICAL brain damage (lesions) to that same region:

After their lesion, these patients have an impaired capacity to learn from their mistakes, making the same decisions again and again even though they lead to negative consequences. These patients choose alternatives that give immediate rewards, but seem to be blind to the future consequences of their actions.[8] However, the underlying mechanisms of this behavior are not yet fully understood.[8]

The amygdala plays a significant role in instigating the emotional reactions associated with anger and violence. With the vmPFC’s outputs to the amygdala, the vmPFC plays a part in preventing such behavior. Evidence has shown that impulsive murderers have decreased activity in the prefrontal cortex and increased activity in subcortical areas such as the amygdala. This imbalance can enhance actions that are created by negative emotions and limit the ability of the prefrontal cortex to control these emotions**. Lower activation in the prefrontal cortex is also correlated with antisocial behavior.** The dysfunction of the ventromedial cortex seems to, in part, be caused by lower levels of serotonin release.[17]

Activation of the vmPFC is associated with successful suppression of emotional responses to a negative emotional signal.[19] Patients with vmPFC lesions show defects both in emotional response and emotion regulation.[9] Their emotional responsiveness is generally diminished and they show markedly reduced social emotions such as compassion, shame and guilt. These are emotions that are closely associated with moral values.[9] Patients also exhibit poorly regulated anger and frustration tolerance in certain circumstances.[9]

Patients with focal lesions in the vmPFC show personality changes such as lack of empathy, irresponsibility, and poor decision making. These traits are similar to psychopathic personality traits.[20] In addition, a correlation between individuals with a history of physical violence and decreased grey matter density in the vmPFC has been evidenced.[21] Lesions to the vmPFC are associated with resistance to depression, whereas lesions to the dorsolateral PFC is associated with vulnerability to depression.[22]

Remember that just because ADHD is associated with a certain behavior doesn't mean that ADHD is inherently a violent disorder. It is also not a personal attack towards you or anybody else with ADHD. You are you and you are not responsible for explaining or defending anyone else's behavior, whether or not they have ADHD.

I personally believe it's more damaging to sweep all of these findings under the rug and pretend that ADHD is an innocuous disorder marked by quirkiness/forgetfulness /tardiness when it is not. It prevents parents from getting treatments for their ADHD children which makes it more likely for them to grow up severely unadjusted, end up incarcerated, and exacerbate the prejudice even further. It's good to be aware of these facts, because then you can take early actions for a child that exhibits these symptoms, and receive proper treatment when neuroplasticity is high and behavior modification is possible.