Hi omkar192,
Thanks for using Apple Support Communities! I see you're having an issue logging in with your Apple ID on your Mac and I'd like to do what I can to help out.
You didn't mention which macOS you're using, but since you mentioned iTunes, that would indicate macOS Mojave and earlier.
Are you following the steps as shown in the Sign in with your Apple ID article? iTunes > Account > Sign In. Enter your Apple ID and password. Click Sign In.
If so, restart your Mac, and then try again.
If you are still not able to log in, what happens when you try? Do you receive an error message? What does it say? (Please don't include any personal information)
Thanks!