The film Child's Play (1988) was followed by several sequels including Child's Play 2 (1990), Child's Play 3 (1991), Bride of Chucky (1998), Seed of Chucky (2004), Curse of Chucky (2013), Cult of Chucky (2017) and a reboot, Child's Play (2019). I haven't watched all of these movies, so I am not sure if you need to, to get the references that the TV series will make. If you want to invest the time to do your homework before the TV series is released, here is where you can find the movies.
Child's Play (1988) Amazon Prime & fubo tv
Child's Play 2 (1990) SYFY & Netflix