Parker Matthew Booth is Seeley Booth and Rebecca Stinson's son. Four years old at the start of the series, Parker and Booth are very close. He is currently under custody of his mother. Rebecca threatened to never let Booth see Parker during Season 2 when he investigated her boyfriend Drew intensively (although in the following season 2 episode, Rebecca and Booth have a short fling when she and Drew are not seeing each other.)
In Season 3's Christmas episode, Parker doesn't get to spend the day with Booth as is typical and has to stay with his mother and go skiing with her and her boyfriend Brent in Vermont; Parker has said that he hated Brent, which his mother believes to be a result of Booth's influence.
In the fourth season episode "The Hero in the Hold" Booth reveals that he named Parker after his spotter, a friend who was slain in the line of duty. In "The Twisted Bones in the Melted Truck", in season 6, Parker names Wizards of Waverly Place as his favorite TV show.
In episode 10 of Season 7, Parker returns from England to visit Booth and his new half-sister, Christine. Booth and Brennan are both apprehensive about how Parker will react to Christine, and their worries appear to be justified when Parker starts locking himself in his room and cutting up family photos in what appears to be a fit of jealousy.
However, at the end of the episode, it is revealed that Parker loves Christine very much and was actually building a mobile which incorporated all of these items, which he hangs over her crib.