Hi, would you please tell me what's the difference among:

  • Did you have supper?

  • Did you have supper yet?

  • Had you supper yet?
My turn.

  • Did you have supper?-- 'Did you eat before now?'
  • Did you have supper yet?-- 'Did you eat before now?-- because I may invite you to supper.' (Yet & already are common with simple past in AmE at least. Yet is used in negative statements and questions.)
  • Had you supper yet?-- Not English any more. It may have worked in 18th century English as an inquiry about eating before another past event.

These have different inplications:

Didn't you have supper yet?-- I thought you did.

Haven't you had supper yet? -- I thought you did.
* Did you have supper? - Asking if the person has attended supper.
* Did you have supper yet? - As far as I know , that`s grammatically not correct.
* Have you had supper yet? - Asking if the person will attend supper.

Hope that helps.
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I think "yet" is usually used in the negative statements. If you want necessarily use this word may be you can say this way:

Didn't you have supper yet?  
Haven't you have supper yet? 
 Mister Micawber's reply was promoted to an answer.