I have applied SSI (for a total disability), and received a letter from the AG stating how much will be taken from my check, with the SS administration as my "employer"... how do they know, and does this mean I am eligible?

I'd help you best I can but I don't know what ag is

"AG" is often the acronym for "attorney general". Attorneys general, or their offices, are responsible for collecting child support in some places.

But that doesn't quite ring true either, and doesn't answer the question of how they would know without the OP knowing.

Yes they can and will take child support out. I'd call or check the soc sec website to find out where you are in the process.

SSI is state welfare disability.
SSDI is federal disability for those with work income.
SSI might be granted while SSDI is pending, and if a lump sum is paid retroactively, SSI gets what they paid you back.
Child support deductions are different in each case.
You need to tell us exactly and accurately what is going on.