Three given names, the second being my calling name: what to put on paper? I have three given names, say Adam John Isaac. Furthermore I have one family name, say Harris. (The names are not my own, but the initials are.) On this website, I read that I can freely choose which names to put on a paper.

My first given name is not the name that I'm actually known as. Therefore, it feels a bit strange to put Adam J.I. Harris on a paper.

In other papers, I often see people placing initials between their (first) given name and family name. So far I have never seen initials before the first given name, like A. John I. Harris. This looks strange, in my opinion, both because an initial before the given name is uncommon, and it might be read as the word 'a' instead of the initial 'A.'.

Now I've been thinking of using John A.I. Harris on the paper. This way all my names/initials are there, and it looks less strange. Furthermore it's kind of funny, as I'm an AI student.

Another option would be to just stick with my calling name and family name: John Harris.

Do you have any thoughts on this? Can the initials A.I. be seen as some (stupid) joke, so could I better leave them out? Or doesn't it really matter at all, and should I just pick an option?
I would not base such a decision on the fact that it is funny or not, as funny depends by the person that reads.
Naming it is not a big issue as long as you are consistent during all your career. 
I would suggest you to pick up one of your three names, your surname and use the composition of them. As far as i understood, you are known as John Harris, so just go with this.

Cheers!