This is not an uncommon question or build. Far from ideal, but not uncommon, and most of them end up with something like a small front hub and controller, and a small battery mounted somewhere like on the seatpost. The OP isn’t providing any details, so absent that, we can fill them in any way that would make sense to us (e.g. guess 100mm front hub spacing, etc.).
The criteria is a small lightweight hub. Investing so much more effort, or typing, on a question where so little effort is demonstrated by the OP seeking the help, only makes sense if you’re applying for sainthood. We all know the build will likely be a short distance, flat ground bike, but still more fun than pedaling without assistance; and not a long distance, off-road, hill climbing, cargo beast, but still fun.
The other problem with going the 20 questions route, is that you’ll eventually land on the perfect components to meet all of the criteria, then inevitably, with greater that 50% probability, the cost will be beyond the unstated budget.