Just 24 hours following the fourth developer-only betas of iOS 10, macOS Sierra, tvOS 10 and watchOS 3, Apple on Tuesday morning has made the latest beta of iOS 10 available to public beta testers who are singed on the Apple Beta Software Program. If your device is registered for public betas, runs a prior iOS 10 beta and has a proper configuration profile installed, iOS 10 Public Beta 3 should appear in Settings → General → Software Update.
iOS 10 Public Beta 3 and developer-only iOS 10 beta 4 contain the same features.