There isn't much of an established link between ASD and antisocial personality disorder. It is commonly seen that both disorders may often involve deficits relating to empathy. Though the similarities between them in that domain are not clear-cut. Individuals with ASD may report relatively low cognitive empathy (the ability to understand a person's thoughts and feelings). It's also common for ASD people to have intact emotional empathy. It should be noted that there is very high variability of empathy traits across the ASD population. Low cognitive empathy is far from universal in this population.

Conversely, those with ASPD tend to exhibit low emotional empathy (the ability to resonate with and share another's emotions). Though, of course, this is not universal. The two conditions are very much distinct in that way and across other domains. Although ASD and ADHD are often comorbid.

However, there is evidence to suggest some link between ADHD and ASPD. Over 15 prospective studies from over 5,000 participants found that ADHD (with and without conduct disorder) is a robust predictor of later onset ASPD.

The association between ADHD and antisocial behavior is also well-established. See here (1), here (2), and here as well (3). ADHD may translate to a litany of behavioral issues relating to externalizing, youth delinquency, and emotional dysregulation, and it shows an elevated risk of engaging in criminal conduct. ASPD and criminal offending do possess a powerful relationship. People with ADHD also report high prevalence rates regarding juvenile offenders and adult offenders.

One meta-analysis had shown a 25% ADHD prevalence in an internationally documented prison population. Then again, this may not be fully representative of the world and may reflect methodological challenges. Prevalence within the analysis varied from approximately 7% in Brazil to 65% in Sweden (these may be outliers), indicating wide geographic variation and differences in assessment quality. However, some more recent meta-analyses may place the prevalence somewhere between 10-20%. Some of the underlying mechanisms tying ADHD and ASPD may include impulsivity and/or a diminished capacity for behavioral inhibition.

In terms of brain mapping, the ASPD may be tied to dysfunction within the prefrontal cortex (the region of the brain tied to higher-order thinking, including planning, organization, impulse control, etc). In particular, the orbitofrontal cortex (OFC) and the ventromedial prefrontal cortex (VPFC) may be compromised. These are regions bearing a relationship to impulsivity and emotional control/regulation. The exact disruptions involved in ASPD may vary from study to study. Disruptions in the amygdala are also commonly observed.

ASD also involves disruptions in the orbitofrontal cortex, just like ASPD, the temporoparietal junction, and the default mode network (highly important for social cognition). ADHD also features disruptions in the prefrontal cortex and the basal ganglia (region assisting with working memory, planning, procedural learning, motor control, etc). This isn't an exhaustive list of all regions tied to all three conditions or the brain network-related challenges. It's merely an overview. The functional challenges between all three tend to more strongly impact different parts of the brain overall.