Baldwin has famously portrayed Trump on Saturday Night Live.
Thomas Wayne, in the comics, is gunned down alongside his wife Martha Wayne in front of their son Bruce Wayne which later inspires the boy to become Batman. Thomas Wayne is normally presented as being a physician and a philanthropist within Gotham City.
Joker, from director Todd Phillips (The Hangover, War Dogs), who co-wrote the film with Scott Silver, is set to arrive in theaters on Oct. 4, 2019. Production will begin in September, Deadline reported.
Joker is described as being a gritty character study with a dark tone. The film will take place outside of DC's extended film universe and would help launch a new DC Comics banner at Warner Bros. that will allow the studio to tell unique comic book stories using different actors in the the title roles.