I am making a Linux application using Python3 and Qt5. When user will install this application, It will create some files in /usr/share folder. To create the files the application needs to have root access.
I plan on having the application show a prompt box to user and user will enter the root password to give root access to the application. But I don't know that how can I give root access to the application by using that password?
This is a world of pain. It's certainly possible to have an application that runs as a normal user carry out certain actions as a privileged user, but I always feel that the need to do this suggests that installation and maintenance hasn't been thought through properly.
To elevate privileges, and assuming the "sudo" isn't appropriate (it probably won't be in this case), you will either need to use an operating system tool that does the job (prompting for credentials and then running something), or implement a helper for your program that has suid attributes on its executable.
I expect all Linux systems have access to "su", but the standard su doesn't have a graphical interface, which is a drag for GUI programs. You can collect the user credentials in your application, and then pass them to su (which is fiddly), or you can use one of the various graphical su-type utilities such as gksu. Of course, that only works if those utilities are available on your platform.
If you go the route of providing your program with a suid part that handles the work that needs elevated privileges, you need to be inordinately careful about security -- how you collect the credentials, how you verify that intruders can't do things they shouldn't, etc.
Frankly, it's a can of worms. I would think that it's nearly always better to provide your application with an installation or maintenance module that has to be run as root. That way all the hard work gets done by the platform.