If you list the child as living in your home more than half the year when the child does not live in your home more than half the year you are breaking the law.
If the child lives in your home more than half the nights of the year, you are always allowed to file as head of household. The difference is whether you are filing head of household with a $2000 child tax credit or head of household without a $2000 child tax credit.
If the child does not live in your home more than half the nights of the year, you must always file as single. The difference is whether you file single with a $2000 child tax credit or single without a $2000 child tax credit.
Either one of those situations certainly might call for the need to adjust your W-4. If you only filed one W-4 and indicated that you had no dependents, then you would break even on the years you don’t claim your child and get a very large refund on the years you do claim your child. If you want to more or less break even every year and get the extra money in your paycheck during the year instead of as a refund, then you would need to file a new W-4 each January to account for the situation that you expect on the tax return at the end of that year.
