Learn English – Is there idiom for searching something that might not exists

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I come from Bulgaria and we have a proverb that says (translated one to one) "You're searching calf under the ox." which literally means that I am searching for something that might not exists.

Example usage: "Stop interrogating Mary already, she's obviously not guilty, don't search for calf under the ox."

Is there idiom with same meaning in English as well?

Best Answer

"On a wild goose chase" might work.

Cambridge Dictionary gives this definition:

a search that is completely unsuccessful and a waste of time because the person or thing being searched for does not exist or is somewhere else:
After two hours spent wandering in the snow, I realized we were on a wild goose chase.

The phrase finder has an article on the history of the phrase. Here's an extract:

Our current use of the phrase alludes to an undertaking which will probably prove to be fruitless - and it's hard to imagine anything more doomed to failure than an attempt to catch a wild goose by chasing after it. Our understanding of the term differs from that in use in Shakespeare's day. The earlier meaning related not to hunting but to horse racing. A 'wild goose chase' was a race in which horses followed a lead horse at a set distance, mimicking wild geese flying in formation.

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