My discipline is Telecommunication engineering and I am writing a paper for an IEEE journal. I want to cite an invited paper published in IEEE Transactions on Information Theory. My question do I need to mention in my citation that the paper is invited? If yes, how? As part of the original article name or the journal name or somehow else? Same with correspondence papers which are not full length articles, but short ones on some emerging area. What does IEEE say about it?
No, cite it as you would any other paper. You do not mention the paper status (“invited paper”, in your case; “review paper”, “perspective”, “editorial”, etc.) in the citation, unless that is formally part of the title (which it typically is not), or unless the citation style explicitly calls for it (IEEE does not, and I know no citation style that does).
In IEEE's templates and LaTeX classes, the only place which mentions invited papers is a command to indicate when your paper is an invited paper (here for IEEEtran):
Special paper notices, such as for invited papers, can be declared with: