How to attach horizontal wood fence posts at an 15 degree angle to a 4x4 post?
So, if I understand correctly, you have a 75 degree or 105 degree corner.

I wouldn't butt an angle cut fenceboard into the post, as the amount of fenceboard that holds a screw is pretty modest. This would be prone to failure.

You could pad your post with a small strip of wood so that your fence boards hit the corner of the post and then are supported on the strip. (The fenceboards would overlap the post.)

(Edited out part about cutting the post, as there's a high probability that the post is PT.)

If it was a 75 degree angle and you felt lazy, you could just overlap the fenceboard and put screws in where the fenceboard hits the corner of the post. I wouldn't do this if you had a 105 degree angle for the aforementioned problem of putting screws through the ends of fenceboards.

Plan your butt joints to overlap nicely and you won't have to worry about putting fancy 15 degree angles on the ends.