All three are correct, however number two (“I haven’t any sister”) is almost never used in contemporary English. In today’s English, “have” is only inverted if it’s an auxiliary verb (used to form the perfect aspect). Note that choices 1 and 3 are singular, implying that the original question dealt with whether or not you have a sister at all. If the question dealt with how many sisters you have, you would use the plural “I have no sisters” or “I don’t have any sisters.” Yes, in English, “zero” can be singular or plural, depending on the expectation.

The 2nd and 3rd ones are incorrect or unnatural. When using the word "any" the noun following it must always be plural. #2 is incorrect for that reason, but also because when making a negation with the word "not," the helping verb "do" must also be used. #3 would be correct if you made the object plural, so the resulting sentence would be: "I don't have any sisters." "I have no sister(s)" and "I don't have any sisters" are both very natural ways of expressing this concept. I hope this helps! Please let me know if there is anything else that you need.

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