Can the person, example my mother be claimed as a dependent since she lives with me be claimed as my caregiver for my kid, i pay her weekly for the care of my daughter?

[SweetieJean]

No.  See Limits on who can provide care:

https://turbotax.intuit.com/tax-tips/family/the-ins-and-outs-of-the-child-and-dependent-care-tax-cre...

[drifter777]

I believe the threshold to claim her as your dependent is whether you provide more than 50% of her support. If she lives in your home I think you're there unless you are charging her rent.