I've done some searching and found some interesting links (1. How many spaceships would it take to block the Sun from the daylight side of the Earth? and 2. https://www.quora.com/Does-the-International-Space-Station-throw-a-shadow-on-the-Earth), but I'm still unsure exactly how to work this out, or if the idea is feasible.
In this story setting, a certain type of entity that has an aversion to sunlight wants to demonstrate their domination of the Earth by constructing a sun shield in orbit large enough to put an entire city into shadow. In terms of size, let's say Vancouver.
Link 1 above would suggest using something huge at Lagrange Point SEL-1, but my setting is kind of near-future, so I think something a lot smaller in geostationery orbit would be more feasible. Link 2 above suggests that, say, a solar sail of 3,200km would be the minimum size required to cast a shadow on the Earth, but how big would that shadow be? And how big would the solar sail need to be to cast a 100% UV-proof shadow of about 50km - either squared, or a 50km wide circle? (I've gone with 50km so there is room for error and drift without the city's residents being torched at the smallest slip-up, but if that's not required then I'm happy for it to be smaller.)
And then, once I've worked out the size of the solar sail (with attached space station for maintenance workers), how best to keep it in position so the shadow stays above the city? Assume resupplies of oxygen and fuel are possible, but something like the (now disproven?) M-drive that can just use energy harvested via the solar sail would be nice and neat too.
First time asking, so I hope I've kept it clear enough.