For the TV series:
No one. The character was never based off of anyone real and was never intended to be.
For the motion picture starring Mel Gibson:
His character of Bret Maverick was based off of the character with the same name from the 1959 TV series "Maverick". The TV Bret was played by James Garner who played Zane Cooper in the motion picture. Reading up on the movie reveals that Gibson's Bret is actually named Bret Maverick Jr. - the son the the Bret from the series.
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