I would try running it some cleaning solution in an ultrasonic tank to see if you can loosen it. You could try drilling it out, or laser welding something to it to help turn it out.
Or, find a replacement...I’ve had to get them mad on occasion, when nothing else would work.
Frequently, the screw for the ratchet wheel is a left hand thread. Most watches use a screw with a right hand thread in this position. If this screw is a left hand thread, on occasion the screw might be broken off in the arbor when someone forces the screw in the wrong direction. Try “teasing” the screw out by “tickling” it clockwise, rather than counter clockwise.
Here are a few steps that may help you remove the broken ratchet screw from your Minerva movement:
Apply penetrating oil: Apply penetrating oil to the area around the broken screw. Allow the oil to sit for a few hours or overnight to help loosen any corrosion or debris that may be holding the screw in place.
Use a screw extractor: If the broken screw is protruding slightly from the arbor, you may be able to use a screw extractor to remove it. Choose an extractor that is slightly smaller than the diameter of the screw and gently turn it counterclockwise with pliers or a wrench until the screw comes out.
Drill and tap the screw: If the screw is broken off below the surface of the arbor, you may need to drill into the screw to remove it. Choose a drill bit that is slightly smaller than the diameter of the screw and drill straight down into the center of the screw. Then, use a tap to create new threads in the hole you just drilled. You may need to repeat this process several times with increasingly larger drill bits and taps until the screw comes loose.