To set off a quote inside a quit what punctuation mark should you use

Use single quotation marks inside double quotation marks when you have a quotation within a quotation.

Bobbi told me, "Delia said, 'This will never work.'"

When you have a quote inside a quote, you'd use a single quotation mark (') for the quote inside the quote.

Here's an example:

My mom said, "Your teacher said: 'homework is due on Monday.' You should finish it tonight."