How will SS compensate if I quite my job to care for Mom?

You really, REALLY need to read the experiences of others who have quit their jobs to care for elderly parents. There are plenty on the site and few of them are good experiences! I am not telling you what to do! But you do need to educate yourself before you do something that you can't take back!

I usually recommend that people not quit their jobs unless they are wealthy enough to do so. The reason is that you will lose not only your paycheck, but retirement benefits down the road. Most of the time you don't know how long you will have to caregive, or if you'll be able to find a job after you finished. If you can't afford to quit your job and your mother can't afford to pay you a good salary, you may want to explore other options first. Setting yourself up for living in poverty would not be the best thing, given that there are other options that may work.

SS does not compensate caregivers. They are not an employer.

If your mother can afford to pay you, you can report it as self-employment income, pay taxes, and continue to build your SS history.

Is this what you are asking?

If you're old enough to collect Social Security, you can start collecting. Other than that, there's nothing that I know of.