Ozone is not mentioned in the [synthetic techniques reported by Wikipedia](https://en.wikipedia.org/wiki/Periodic_acid#Synthesis), citing [Greenwood and Earnshaw[1]](https://doi.org/10.1016/C2009-0-30414-6).

Summary:

* Orthoperiodate ion, $\ce{IO5^{6-}}$, is obtained by alkaline oxidation of iodate either electrolytically on a lead dioxide anode or chemically with chlorine.  The product may then be acidification to $\ce{H5IO6}$. Alkaline conditions favor formation of the oxygen-rich orthoperiodate ion; note the inclusion of hydroxide ions in $\ce{IO3^- + \color{blue}{6 OH^-}->IO6^5- +3H2O +2e^-}$.

* Metaperiodic acid, $\ce{HIO4}$, may be obtained by dehydration of the ortho acid.  This can be accomplished by heating to 100°C (but below 150°C) or by treatment with dilute nitric acid.

**Reference**

1.
Greenwood, N. N.; Earnshaw, A (1997). Chemistry of the elements (2nd ed.). Butterworth-Heinemann. p. 872. doi:10.1016/C2009-0-30414-6. ISBN 978-0-7506-3365-9.