My text messages keep popping up on my child’s iPad. How can I get it to stop?

As moneesh_64 suggests, your child needs her/his own Apple ID.

Help your child set up an iPhone, iPad, or iPod touch - Apple Support

Before setting up that new Apple ID on your child’s iPad, it needs to be thoroughly cleansed as follows:

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

Maybe you Apple ID is being used in that iPad. You should sign out from iPad.

What software update runs on that iPad?