Baby birth certificate under my wife iqama

Assalam alaikum .will you plz tell me if I can apply for my baby boy birth certifiacte who born in saudi .under on my wife iqama. She is working with differnt sponser. Not under me.we are indian nationlity

Birth certificate has details (name, iqama# and nationality) of both from parents.
And that has nothing to do with the sponsors.

Only father can register (do tableegh)  and get it, mother can't.