Exorcist Timeline
1947 - Dominion: Prequel to the Exorcist
1949 - Exorcist: The Beginning
1975 - The Exorcist
1976 - The Ninth Configuration
1979 - Exorcist II: The Heretic
1990 - The Exorcist III: Legion
2016 - The Exorcist 1x01, "Chapter One: And Let My Cry Come Unto Thee"
2016 - The Exorcist 1x02, "Chapter Two: Lupus in Fabula"
2016 - The Exorcist 1x03, "Chapter Three: Let 'Em In"
2016 - The Exorcist 1x04, "Chapter Four: The Moveable Feast"
2016 - The Exorcist 1x05, "Chapter Five: Through My Most Grievous Fault"
2016 - The Exorcist 1x06, "Chapter Six: Star of the Morning"
2016 - The Exorcist 1x07, "Chapter Seven: Father of Lies"
2016 - The Exorcist 1x08, "Chapter Eight: The Griefbearers"
2016 - The Exorcist 1x09, "Chapter Nine: 162"
2016 - The Exorcist 1x10, "Chapter Ten: Three Rooms"
2017 - The Exorcist 2x01, "Janus"
2017 - The Exorcist 2x02, "Safe as Houses"
2017 - The Exorcist 2x03, "Unclean"
2017 - The Exorcist 2x04, "One for Sorrow"
2017 - The Exorcist 2x05, "There But for the Grace of God, Go I"
2017 - The Exorcist 2x06, "Darling Nikki"
2017 - The Exorcist 2x07, "Help Me"
2017 - The Exorcist 2x08, "A Heaven of Hell"
2017 - The Exorcist 2x09, "Ritual & Repetition"
2017 - The Exorcist 2x10, "Unworthy"
2018 - The Exorcist: Legion VR
2023 - The Exorcist: Believer
Both of the prequels are the same story. However, almost every single scene is completely different footage, following simular events but with different actors and character names. Only the flashbacks are the same, and we can combine those and take both as the exact same events. Essentially, we can take both prequels as canon and the first prequel is a "sequel" to the second prequel.
The Ninth Configuration is canon in the books at least. Billy Cutshaw, the astronaut from The Exorcist, appears in the movie. He's recast but it's fine.
The new movie retcons the TV series as an alternate timeline. Either only the original movie counts in that reality or it's a branched timeline. Probably the former, since I think it placed the first film in 1973 (edit: I was wrong, the month is different). I haven't seen the whole series, but maybe you can argue that the MacNeil family are separate individuals to the film characters who might have known separate versions of Karras and Merrin. This is probably unlikely.
I think I've gone over this before, but I learned about the extended cut of The Exorcist III and I love that film.