Queen clipping is an old practice, and in my opinion barbaric, used by some beekeepers in which the queen’s wings are clipped on the tips to prevent her from flying with a swarm but also indicates her age depending on which wings are clipped. The right two wings are clipped on even years and the left two on odd years. Queen clipping to prevent the queen from flying with the swarm does not prevent swarming. Usually the bees will push the queen out of the hive onto the ground, then abandon her, and possibly swarm with a virgin queen.
When selecting paint, only use water soluble acrylic paints to prevent harming queens. Don't use permanent, harsh, or toxic paints such as model paint. Paint pens are not as good as using a tiny paint brush and dipping it in paint. Paint pens are a pain to get the paint out, cost more, and don’t have as much paint as a bottle.
To prevent queen rejection and queen balling, it’s best to mark queens before introducing her to the colony. Bees can be very picky and can reject/ball the queen for a number of reasons such as broken legs, wings, antennae, etc. The paint smell can temporarily alter the queen’s pheromone or smell. If you must mark the queen after she’s been introduced, allow the paint to completely dry or use a queen cage to reintroduce.
Queen tubes with foam plungers are best for marking queens. Very gently push the plunger up to pin her gently near the plastic cage top and dab her thorax with paint. Release plunger slightly to allow her to move around. Allow the paint to dry before handling her to prevent smearing. 
It takes great patience and a delicate touch to mark queens. Since drones don’t have stingers, it’s best to practice marking drones to learn how to handle bees with your bare hands. It is possible to be stung by a queen, however, if handled correctly, reduces your chances of being stung. I have marked thousands of queens and have never been stung by one.