Is it CTS registratin no? or the red number on the right top of certificate?
The number on the top of the right side
I-864:
Part3. Information on the immigrants you are sponsoring.
8. I am sponsoring the principal immigrant named in Part 2 above. YES
Yes
9. I am sponsoring the following family members immigranting at the same time or within six months of the principal immigrant named in Part 2 above. Do not include any relative listed on a separate visa petition.
I am sponsoring both my mother. should I put my father's name here? (I'm filling a separate visa petition for him at the same time)
Yes, put your father or mother name here. Also, do same thing on another one.