If I rent the basement in my mother’s house with my son. Everything is split 50/50. I am filing head of household. Can she claim both me and my kid because we live here.

[NCperson]

if you earned more than $4200, then she can't claim you. 

did she provide more than half your support? if she did, she can not claim you. 

[DeanM15]

No she can not claim you if you are filing Head of Household (HOH).

If you are filing HOH, then you are claiming your own exemption as well as your son's exemption. Once you have claimed those exemptions, they cannot be claimed by another. 

To file HOH, you must:

• Pay for more than half of the household expenses
• Be considered unmarried for the tax year, and
• You must have a qualifying child or dependent.

You can find out more about the Head of Household filing status here.