My child stays with me at least 50% of the time, do I still have to give child support to the mom?

CA resident. Never married. I understand that I'm at least responsible for his health/dental insurance (which what I've been taking care of), but does the mom require more? I provide just as much as she. She's married & has another child. I'm single. I have huge projects I want to do to benefit my son (11yrs old), but it would require every cent to put into? Want to file for joint-custody stay, but trying to avoid all drama possible.
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AS far as I know, when parents have 50/50 custody, they do not have to pay support. Child support is to make up for the time that you are not there to provide housing and clothing costs.
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