Matching is of course an important factor in choosing a Psy.D program, at least. I'm a veteran and was wondering if I would get veteran's preference when applying to VA internships. Thanks for any help.
Not 100% sure but I think veteran's preference only applies to positions that originate from VA HR/USAJobs whereas the VA's educational branch covers training.
Regardless, for cover letters and hopefully interviews, you can definitely discuss how your service may relate to your motivation for VA training, future career prospects, etc to demonstrate possible fit with VA sites you're interested in.
It applies at some VAs in an informal way. Some committees will definitely boost an application somewhat if they are a vet. It's usually a small bump, it won't help at all if the overall application isn't good, though. If the ranking decision is between two similar apps and a vet is one, it'll get the upper hand. If the app is from a diploma mill, won't help you at all.
Yes, if you were applying for a permanent VA job that's searchable on usajobs.gov, you'll be asked some questions about veteran's preference and then assigned a point bump.
But predoctoral internships and postdoctoral fellowships are organized by the VA's educational branch and trainees apply through APPIC and are not technically classified as full VA employees but in some type of hybrid classification.
For internship, VA HR only gets involved once the selection has been made by the training program for onboarding tasks, hence the informal boost that may/may not exist depending on where you apply that @WisNeuro referred to.
EDIT: in general, I imagine that many VA internship programs would love to have trainees who are veterans since that tends to be rare.