like less sunlight around the poles would be good. if we put it in orbit close to the sun we may not need it to be that large. we can keep it in good position with RF cavity thrusters and mini nuclear reactor maybe. is it possible to do?
Probably not in the next 100 years at least.
I assume you mean just using a sheet of material to shade portions of the earth. To start, because the Sun is much bigger than the Earth, and it radiates in all directions from its surface, the shade sheet would be most size-efficient if located close to Earth. Still, any shade sheet would need to be the same size or larger than the Earth’s side-on profile for the shaded area. This sheet would probably be in Sun-synchronous Earth orbit (please correct me if this is not a stable orbit) to avoid relative movement.
The poles would be smaller in profile, as they are angled away further from the sun. This would decrease necessary area, but the sheet would still need to be the same size in one of the dimensions. Also, the earth’s 22.5 degree tilt means that the target area would change through the seasons.
The overall concept you describe is possible and would have the effect you're trying to a achieve, but with current technology and launch capabilities it is still science fiction in the far future.
For your "sun regulator" I would advise to have a lot of smaller satellites which decrease the overall radiation which reaches earth instead of one big reflector darkening one area at a time.
So basically a Dyson Sphere/Swarm around the sun or earth. This would still allow light and other radiation to reach the earth or all the other planets, just less. Building this mega project around the earth does make it more achievable and prevents that the outer planets get even less light than they already do.
Extra points for your constellation if it does serve an additional purpose, apart from sun shading. How about to use all those satellites for power production or reflecting the sunlight somewhere where we need it (other planets, etc.)?.
But coming back to what is currently achievable the best options would be an extending/unfolding solar sail kind of solar panel*. This way we can launch them on our current generation of launch vehicles. Something like this JAXA prototype (video of people unfolding is for scale) for their asteroid probe.
For further "research" I can recommend Issac Arthur's youtube channel, he does quality content about science fiction related to space. He does have videos about power satellites, dyson spheres and a lot of other topics which fit your question.
*I do not know about those sails being easily able to maintain a orbit over a long time as those are literally solar sails. Would electronic propulsion with xenon be able to keep those satellites in orbit for a long time?
Blocking out sunlight from reaching the earth is tricky at best, impossible at best, and extremely irresponsible.
You'd kill all plant life, turn the planet into an eternal (well, at least until your sunshade fails) ice ball that can't support life.
You'd also plunge the planet into eternal darkness. And there'd be no solar power to light and heat your house, no wind power either as the winds on our planet are largely driven by solar input causing heat flow between warmer and cooler areas, all of which would stop as the planet becomes a thermodynamic equilibrium at far below the freezing point of water.
Theoretically, what you're saying could be taken into consideration. But practically talking, it's close to impossible.
First of all, blocking the sunlight or even reducing the amount of sunlight that comes into the Earth can be catastrophic and is something I don't think anyone would want to do.
Secondly, if we even wanted to give this a shot, we'd need something huge to do it, probably the size of our planet, or even bigger. Which isn't easy to build.
We'd need some material that can be suitable for this and also in a huge quantity such that we can build a shield/screen of the required size, which I don't think can be arranged, at least as of now.
Now, moving on to your theory of keeping it in an orbit near the sun, that's totally science fiction as even if we build something that huge, it won't be possible to transport it there and the orbit would be really large considering the size of the sun. Also, the closer you keep it to the sun, the larger it needs to be, and that size is also something which can only be said as a fantasy. The temperatures near the sun won't let the material last really long either.