Legal Question in Family Law in California

They're a citizen of the state in which they are born, until they move to another state with the intention to reside there. By the way, Texas is part of the United States, so he is a U.S. citizen as well. But you can still feed the child great Texas style cooking.

A child's "citizenship" other than national citizenship is irrelevant. A child's residence is what matters. What state, and for that matter what county, city, school district, etc., a child legally resides in depends on specific laws related to why the residence is important. So for example, for child custody and support jurisdiction, where the child "habitually resides" is what is relevant, and generally it is where the child has resided for the last six months (a few states may have different rules but that is the most common). For school district residency, most states allow you to register in a district as soon as you physically live there. But of course if his parents are Texans, they can always call him a Texan if they want. It just won't have any legal effect.