The show has garnered media attention after pre-production clips were leaked to YouTube, portraying Shawty Lo referring to the childrens' mothers with nicknames like Jealous Baby Mama, Baby Mama from Hell, and Shady Baby Mama, ABC News reported.
The cable show also portrays the strife between the 36-year-old rapper's multifaceted family and his 19-year-old girlfriend.
Several organizations have urged for the show to be canceled, including Change.org, where there is a petition circulating that already has more than 30,000 signatures.
The petition called the show an "attack not just on African-American parents and children but all parents and children."
The Parents Television Council is also involved and has stated that if Oxygen continues with the program, it will contact the network’s corporate sponsors and also hold them accountable.
Oxygen has said that the leaked video was from a third-party and contains footage that won’t be used in the special. The network also said there is currently no air date for the special and that it is still in the process of selecting a cast.
"Oxygen's one-hour special in development is not meant to be a stereotypical representation of everyday life for any one demographic or cross section of society," Oxygen told ABC News.
"It is a look at one unique family and their complicated, intertwined life. Oxygen Media's diverse team of creative executives will continue developing the show with this point of view."
The network announced the special two weeks ago, describing it in a statement as an "intimate look at unconventional families with larger than life personalities and real emotional stakes."