no psychiatry fellowships are competitive (apart from the non-directly related ones like sleep and pain). it is very much a niche interest, but as it is an academic field, you can assume that showing an interest in this area through electives, research, publications, presenting at the ANPA or ACNP or related meetings would be helpful. there aren't a great many of these fellowships for psychiatrists the main ones are at BWH, Hopkins, UMass, and I believe that UIC and MGH also have neuropsychiatry fellowships. To be distinguished from cognitive/behavioral neurology fellowships which are for neurologists. There is a huge overlap with geriatric psychiatry given dementia is the largest part of neuropsychiatry.
you can actually carve out a lot of time in residency to develop an interest in this if you wish. at my program there are electives in neuroradiology, neuropsychology, sleep medicine, neurobehavior/memory disorders, psychiatric consultation to the neurology/epilepsy service, TBI, autism clinic etc. I have an interest in the more psychological aspects of neurology (i.e. functional neurology) and am setting up a research clinic and can have up to 50% time in PGY-3 and 4 to do this.