Sounds like he wants to fleece you for money. If this were an actual thing, I’m sure it would be well known and tried by everyone who overstayed.
I’m sorry but you do not have a path to a legal status in your situation as of now. When your US citizen child turns 21, they can sponsor you and you can adjust status in the US and the 10 year ban will be forgiven as you are an immediate relative of a US Citizen. If you leave the US at any point you will have to serve the 10 year ban first. A US citizen child will not be able to file a waiver or do anything about it, you will have to serve out the full ban.