Henry Fonda did not receive an Oscar nomination for portraying Wyatt Earp in My Darling Clementine.
Henry Fonda plays the famous and often portrayed Wyatt Earp, but My Darling Clementine isn't really trying to represent the historical Earp nor is it really realizing much of its own vision regarding the man. Fonda would go on to portray a rather negative depiction of an Earp like character in Warlock but in this film, as written, Earp is more of just a pretty standard western hero. The film makes brief mention of his earlier days in law enforcement but they are mostly glossed over in favor of him being a fairly typical hero you'd expect in a John Ford western. He comes in with his brothers to Tombstone with cattle, and is just looking to make a new life for himself much like many a standard heroes. This is only continued when he gets wrong by someone leaving him to have to stay in Tombstone to find the culprits again in a pretty standard hero sort of fashion.
Henry Fonda's performance though does work well enough within this extremely limited version of Wyatt Earp in which every part of him is pretty muted as written. The history of the character is only mentioned without giving any more depth to the man, his brothers are non-entities, and he's barely even friends with Doc Holliday (Victor Mature). In fact they are slightly antagonistic to one another before Holliday helps at the end to get revenge. Even the antagonism between the two is pretty simplified to the point of Earp just saying for Holliday not tell people they need to get out of town. Then there is Earp's romance with the titular Clementine which never amounts to anything more than a few longing glances from Earp since she is far more interested in Holliday than him. This is altogether a pretty thin role and really it's only in the depiction of Earp's vengeance for his brothers that the film illustrates much about the character.
The character is actually pretty much left to Fonda himself since Earp's most defining feature throughout the film is to want to keep the peace despite the rowdy nature of almost everyone around him. Fonda certainly brings the needed presence and command for a part such as his, but really what he adds to most is the slightly humorous touches he brings to his character. It isn't that this is even a funny performance exactly but rather Fonda has this certain ease in all the standard western moments that manages to lighten them up a bit. Now he goes the exact opposite when Earp gets his revenge which is rather brief actually, but Fonda certainly brings the needed intensity when it is called upon him. This is hardly the definitive portrayal of Wyatt Earp by any means, but that's always feels like it is the writing's fault not Fonda's. I don't think I've found that definitive performance yet, but on its own Fonda gives a solid enough leading turn in a John Ford western.