I am trying to detect the jail break on the application startup and don't know how to check for the application other then the cydia like Tweakbox, iNoJB etc are installed or not.
This question is different from other jailbreak question which detect for only cydia app not tweakbox and other is because i want to look all the application like cydia not just only cydia. and other answers in stack overflow are just checking for the cydia application and access for certain files that exist in sandbox
Those apps have nothing to do with jailbreak, full or not. All of them are properly signed iOS apps. For example, GBA4iOS is signed with "Meridian Medical Network Corp." enterprise certificate allowing it to be installed on any device. That violates ToS and can get your account terminated but works.
Given that and the fact that recent iOS versions closed private APIs for getting a list of installed applications, there's no way to achieve what you want. Furthermore, Tweakbox, iNoJB, AppValley are not even apps. They're websites with links to enterprise signed applications. Some of them require you to install configuration profile but its only purpose is to put a web link on the SpringBoard that leads to their website. You can download the profile and check its contents in any text editor, it's just a plist with signature at the end.