Crossword Genius

On the fourth of July, he could have partnered Cleopatra (5)

Ross

I believe the answer is:

anton

I'm a little stuck... Click here to teach me more about this clue!

'the fourth of july he could have partnered cleopatra' is the definition.
The definition suggests a singular noun which matches the answer.

'on' is the wordplay.
I cannot quite see how this works, but
'on' is found in the answer.
The remaining letters 'ant' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for anton that I've seen before include "..... Chekov" , "Boy" , "-- Bruckner, composer" , "-- Chekhov, Russian dramatist" , "Chekhov, say" .)

I've seen this clue in the Evening Standard.
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