I am looking for the formally correct abbreviation of assistant professor. How do I refer to someone in that position in a letter or on a webpage? Is Asst. Prof. Dr. the right title?
In my experience, what comes before professor (e.g. assistant, associate, full) is only really used in formal contexts, and in most other cases simply "Professor"/"Prof." is enough.
And, at least in the sciences, "Doctor"/"Dr." is typically used when that is the highest title.
I've never seen both "Professor" and "Doctor" used together.
So, in your case, I suppose "Prof. X" is good enough.