If it were me, I wouldn't worry about that. The height is fine and is in the normal range. Unless you are very tall and have to bend over to reach the door knob, it's not a big deal. As for the patching, it could be done, but would likely be noticeable, especially over time if the filler started to crack around the edges. The only way to insure it would be unnoticeable would be to pull out the jamb and replace it. I'd let this go....

It’s within the standard height range. I wouldn’t sweat it at all.

You could probably fill the jamb hole with wood dough and sand it smooth. It would take several applications to build up sufficient thickness without shrinkage cracking.

Overall, though, I have to agree with the others that this is a great example of a First World problem. If you don't have anything more critical than doorknob height to spend your home improvement dollars on, consider yourself really, really lucky.

I agree with the others, and would let it go. 3 inches lower, isnt really that big a deal.