Levi Johnston, 19, is the father of 10-month-old Tripp with his ex-girlfriend Bristol, the daughter of the former Alaska governor. The two were engaged to be married, but broke off their relationship in March.
Johnston is seeking joint custody at the end of the month because the Palin family is allegedly making it difficult for him to see his son, he told The Insider.
"It's not working. I'm done," he said. "It's going to have to go to court. They just finally pushed me over the edge."
The relationship between Johnston and the Palins has taken a particularly nasty turn in the last few weeks, with Johnston calling Sarah Palin a hypocrite, and Palin lambasting him for his upcoming nude pictorial in Playgirl.
The Palin camp did not respond to requests for comment. Sarah Palin's lawyer, Thomas Van Flein, told Britain's The Guardian newspaper on Oct. 30, "Other than noting that Tripp's father is always welcome to visit his son, we are unable to respond to these allegations as it is inappropriate to discuss child custody matters publicly."