The meaning of "What have I to do with you?"

2Sa 16:

9 Then Abishai son of Zeruiah said to the king, “Why should this dead dog curse my lord the king? Let me go over and take off his head.” 10 But the king said, “What have I to do with you, you sons of Zeruiah? If he is cursing because the Lord has said to him, ‘Curse David,’ who then shall say, ‘Why have you done so?’ ”

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Perhaps God wanted Shimea to curse David. Abishai didn't dare to talk back to the king.

2K 3:

13 Elisha said to the king of Israel, “What have I to do with you? Go to your father’s prophets or to your mother’s.” But the king of Israel said to him, “No; it is the Lord who has summoned us, three kings, only to be handed over to Moab.”

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Elisha didn't shut the king of Israel up. King Joram wondered about the will of God and insisted on an answer.

14 Elisha said, “As surely as the Lord Almighty lives, whom I serve, if I did not have respect for the presence of Jehoshaphat king of Judah, I would not pay any attention to you.

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2Ch 35:

21 But Neco sent envoys to him, saying, “What have I to do with you, king of Judah? I am not coming against you today, but against the house with which I am at war; and God has commanded me to hurry. Cease opposing God, who is with me, so that he will not destroy you.”

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Neco dismissed Josaiah claiming God's will. Sure enough, he killed him in a battle later.

This idiomatic usage continued to the NT. Jesus asked Mary in John 2:

4 "Woman, what have I to do with you? My hour is not yet come."

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Jesus didn't want to be bothered. That didn't shut her up:

5 His mother said to the servants, “Do whatever he tells you.”

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Jesus consulted God's will, followed through, and turned the water into wine.

Mk 1:

24 [The demon] cried out, “What have you to do with us, Jesus of Nazareth? Have you come to destroy us? I know who you are, the Holy One of God.”

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The demon said, "Please kill me."

25 But Jesus rebuked him, saying, “Be silent, and come out of him!”

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Jesus shut him up.

Mk 5:

7 Crying out with a loud voice, [a demon] said, “What have you to do with me, Jesus, Son of the Most High God? I adjure you by God, do not torment me.” 8 For he was saying to him, “Come out of the man, you unclean spirit!” 9 And Jesus asked him, “What is your name?” He replied, “My name is Legion, for we are many.”

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The demon used the idiom and the name of "God" to avoid confrontation with Jesus, but it didn't work out.

Mt 8:

29 Suddenly they shouted, “What have you to do with us, Son of God? Have you come here to torment us before the time?”

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Luke 8:

28 When he saw Jesus, he fell down before him and shouted at the top of his voice, “What have you to do with me, Jesus, Son of the Most High God? I beg you, do not torment me”

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What was the meaning of "What have I to do with you?"?

Throughout Scripture, the idiom "What have I to do with you?" was a rhetorical device. There was a tension between human intention and the will of God. It was used in the context of the will of God to express a desire to avoid interaction, interference, or confrontation. The result could be positive or negative, depending on the actual will of God.