Can you prune Thuja Orientalis Aurea Nana

You can clip this back a bit and remove one or two branches if necessary - best done in the spring for the overall clipping, but you could remove a couple of branches in the autumn rather than now, preferably nearer the end of September.

Assuming your Platycladus(Thuja) orientalis Aurea 'Nana' still has its lovely rounded oval shape, then any removal of branches is likely to spoil the look completely. As bamboo says give it a light clip over every year in spring or early summer to keep it in check. As this plant is very slow growing, a twenty year specimen would only be about 5 feet high x three feet wide, I'm surprised it's getting to big for its location