It is possible that the child has decided s/he wants to live with dad, at least for awhile, and asked the dad if s/he could move to California. If no court has been involved yet, that could be a good reason for dad to involve a court now.
Just a guess, of course.
Another guess is that dad is in desperate need of money and figures child support is one way to get some, even if the money comes with a kid attached.
Another possibility is that it is a knee jerk reaction to an automatic child support review (if dad is currently paying child support). I can also think of possibly another half dozen potential reasons.
The bottom line is that the only hope dad has of winning this is by a default judgement. And the only hope of that happening is if dad lies to the court AND mom is foolish enough not to address the situation now. It will be a whole lot easier to get it stopped now, then to challenge it after a default ruling.
Mom, you really need to talk to a family law attorney in CA and one in the state you are living in now. I am not saying that you need to hire one right this minute, but you need to consult with one in each state, to get a picture of where you stand and what your options are. It may be that accepting service of the suit and responding that CA does not have jurisdiction and why, and asking that the case be dismissed, would be the appropriate action. The attorneys will advise you.