These have the same meaning, but “worst day of my life” is much more common. If you say “worst day in my life,” people will understand what you mean but it does not sound as natural.

Only "Worst day of my life" is correct. After a superlative, we use OF for plurals and periods of time -she is the best tennis player of all We use IN for singular / places / groups -she is the best tennis player in her team