Suppose a person is speaking and if I want to interrupt him, what can I say?
1)Will you mind mine interrupting you?
2)Will you mind me interrupting you?
3)Will you mind my interrupting you?
What is the correct construction?
Suppose a person is speaking and if I want to interrupt him, what can I say?
1)Will you mind mine interrupting you?
2)Will you mind me interrupting you?
3)Will you mind my interrupting you?
What is the correct construction?
Option (1) is straightforwardly wrong. Don't use it.
Option (2) and (3) are both valid, but are a little stilted. A more natural way would be to say:
Would you mind if I interrupt you there?
Would you mind if I interrupt you for a second?
Can I interrupt you for a minute?
If you're interrupting to add something or disagree with the sentence you can also say:
Can I just stop you there?
And if you're interrupting an unrelated discussion to get someone's attention:
Excuse me, Mr Johnson. Can I have a moment of your time? (esp. to a more senior person)
Excuse me, Mr Smith. Can I have a quick word with you?
Will would normally be used by a native speaker to ask strictly about the future:
Will you mind if I interrupt your meeting tomorrow? I'm going to be late.
Mine is never used as adjective or modifier. You can say "That is your dog; this is mine." not "That is your dog; this is mine dog." In the last sentence, I should say "this is my dog" or use mine without dog (as in the previous sentence).
As said in "Would you mind if I [do something]?" versus "Would you mind me [doing something]?", "Will you mind my interrupting you?" is equivalent to "Will you mind if I interrupt you?" while "Will you mind me interrupting you?" refers to me personally and not to the action.