[1] Who I should say is calling?
[2] Who is calling should I say?
[3] Who is calling I should say?
Examples [1] and [2] don't work because the subject-auxiliary set 'I should' looks like a statement. To get a question, you need to invert them, like this: I should => should I?
I'm not sure what you're asking here, 'what type of question is "Who should I say is calling?" ' The base structure looks like (A) below. (B) is the result of auxiliary+subject inversion, and (C) is the result of two things: (i)
who movement, and (ii) auxiliary+subject inversion.
(A)
I should say
who is calling. <statement>
(B)
Should I say
who is calling? <question>
(C)
Who should I say is calling. <question; requesting the person's name>
'who is calling' is the object of the verb 'say'. 'should' is a modal-auxiliary, and 'I' is the subject. The difference between (B) and (C) in terms of meaning is this. The answers:
(B) Yes, you should tell me the name of the person who is calling me.
(C) Yes. Please tell Max that Casiopea is calling him.
All the best.
