Crossword Genius

As king, I had a child (3)

Ross

I believe the answer is:

kid

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

'child' is the definition.
(I know that child can be written as kid)

'as king i had a' is the wordplay.
I cannot really understand how this works, but
'king' could be 'k' (abbreviation for king in chess) and 'k' is present in the answer.
'i' is within the answer.
'had' could be 'd' (in contractions e.g. 'I'd', 'you'd' etc) and 'd' is found within the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for kid that I've seen before include "Playfully deceive" , "Soft leather" , "Tease; hoodwink" , "Suede" , "Goat - boy" .)

I've seen this clue in The Times.
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