Added to much PS fluid and it started dripping after driving and parking the car in the garage at the end of the day. I drained some of the PS fluid out and cleaned all the mess now is OK and back to normal, no more fluid dripping.
QUESTION: was wondering if this will do or did any kind of damage to the pump?

 

Not to the pump, but make sure it didn't drip and compromise any electrical connections. Dripping brake fluid is what was causing catastrophic fires in Ford F-150s a few years back in the cruise control system. I would worry about PS fluid in the same manner.