Determining if the patient is a true psychopath vs just antisocial (yes, they are different) can be helpful in terms of whether you can actually do something. With the former it will typically become fairly obvious rather quickly if you are looking for it and the treatment is discharge. The latter can be helped if they're motivated and I actually had a couple in residency who did very well for stretches of over a year once other psych problems were stabilized (typically substance problems but also trauma-related disorders). One in particular actually ended up working at the VA I treated him at as a lab tech for a couple years, was really productive, and was liked by a lot of the staff. Malingering is still very common though, and if they're not motivated for change then best option is to safety plan, provide assistance for basic resources, and discharge.
For reading, I like Resnick's papers and chapters on malingered psychosis.