You need a jeweller's screw extractor. Look for for a jeweller's tool supply firm. You will need to look around a bit for it as they are much smaller than the ones you normally find at machine shops.
You will want the type that requires drilling a pilot hole first. They are conical in shape with steep spiral cutting edges that cut into the screw in the pilot hole turning counter clock-wise to unscrew it. Read up on the technique as much as you can before actually doing anything, to avoid a disaster.
The most common cause of stripped screw heads is insufficient pressure on the screw driver that then allows it to slip on the screw head.
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