Verifying third party apps doesn't do anything

When I get a third party app it says it needs to be verified before I can use it but when I go to settings to verify I tap verify and nothing happens. Is there something I can do so I don’t have to constantly reinstall my apps?

It sounds like you're trying to run illegal copies of apps (or more precisely - enterprise signed apps when the membership of the enterprise isn't at all what Apple intended).

Tapping Verify like you do is the correct way to verify apps and will check / log information that Apple uses presumably to decide to contact that Enterprise if they are indeed in violation of their agreement with Apple.

If nothing happens, it's almost certainly due to Apple revoking the developer certificate because it's been used to distribute apps illegally or without a license or with a certificate issued for other purposes.