According to a study, a new medication A3IS (Mycosinate) that slowly releases hydrogen peroxide was found to be about 40% more effective than amorolfine (Curanail, Loceryl, Locetar, and Odenil) after 6-12 weeks of treatment, and 70% more effective at 6 months of treatment. That said, Mycosinate may not yet be available for commercial use.
However, this research did not examine the direct application of hydrogen peroxide on toenail fungus. The Global Nail Fungus Organization does list the substance as a remedy.