Is that correct phrase "No any issues"?

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"No issues"
"I don't have any issues"
"There are no issues"

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It should be: "No issues"; however, you could, instead, say "Not any issue(s)".
We use 'No' for 'Not Any'. For example,
I do NOT have ANY issues. = I have NO issues.
There is NOT ANY issue. = There is NO issue.

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Depending on the context, maybe the meaning you want to express could be closer to: "No worries" / "No problem"