Hello Xeevuwoi46
Your child does not need a ticket, and not registration is needed. There is no guarantee for a free seat on board Swiss transit services, not even for adults. Children below 6 years of age may take their own seat if available; it is considered courteous, if you take the child on your lap if other persons are in need of a seat.
Read more on the seating on Swiss trains here:
https://community.sbb.ch/d/23887-demystifying-seat-reservations-on-swiss-trains-a-comprehensive-guide
Kind regards,
Roland