Quote - When I render this figure it has a white pixel all around the edges of it , when I take it to PSP.
I have tried selecting it and deleting but for some reason it still appears.

 From the view of the image this looks an alpha-channel issue, e.g. you rendered your image with a white background and then composed it with a drop shadow which is black. But i am not sure what your example image actually contains, is this the poser-output or is it the poser-output on a white background with a drop-shadow from a painting application?

Quote -
I have also tried rendering on a black background with no change to this white pixel area.
It sort of seems like this area is maybe transparent to a degree because if I put say a dark blue background behind the figure (or character)  then that color is showing around the edge.

 You mean, on a black background, you still get a white border, but on a blue background you get a blue one? In general if trying to use the the alpha-channel at all, you should always render on a black background (The render-settings contain an option for it). The background must be the "real" background, i.e. a background-object like a backplane will not work). Then save your image in a format that supports alpha channels (e.g. png does, jpg does not). In your painting application it should work then (if given the choice, use "premultiplied" instead of "key", if not it probably works anyway).