Signed 8332 form for future years but i had my child longer in 2020 because of covid 19 do i get to claim hoh?

You need to understand the rules.  Only the parent where the child lives more than half the nights of the year has the automatic right to claim that child as a dependent and qualify for head of household, earned income credit, and a dependent care credit.  The noncustodial parent can only claim the child as a dependent if the custody a parent gives the noncustodial parent assigned form 8332. That only entitles the noncustodial parent to claim the child tax credit. The ability to qualify for head of household, earned income credit, and the dependent care credit always stay with the parent where the child lives more than half the year and those tax benefits can’t be waived, transferred, or shared.

So yes, if the child lived in your home more than half the nights of the year, that child will help you qualify for head of household status. In TurboTax, enter the child, indicate that the child lived with you more than half the nights of the year, answer yes to the custody question and yes that you will be releasing the dependent claim to the other parent with form 8332. TurboTax will not claim the child tax credit for you but will allow the child to help you qualify at four head of household.

But it is also important to understand what happens if the child’s living arrangements change and the child lives more than half the year with different parents in different years.  If the child does not live with you more than half the nights of the year, the other parent can claim the child as a full dependent and the form 8332 that you signed is meaningless. That other parent can claim the child as a dependent and claim the child for head of household and earned income credit, and you can’t claim anything unless the other parent gives you a form 8332.  The primary claim always goes where the child lives more than half the nights of the year, even if it changes from year to year and regardless of any written custody order.