Only once in baseball history has a father played with his son. It happened in 1990 when the Mariners traded for Ken Griffey Sr. and placed him in the outfield with his son, Ken Griffey Jr.
In their first game together the Griffey’s hit #2 and #3 in the Mariners’ lineup, and they both got singles in their first trip to the plate in their first game.
Here’s a video about the Griffey’s from 1989.