No as Grammar Geek told you. It is wrong, if you are asking about someone's father's job,you can use the following alternatives.
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What does your father do?
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What is your father's job?
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How does your father make a living?
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how does your father pay the bills?
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What does your father work?
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what is your father's profession/occupation?
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and many other alternatives but not what is your father?