Visa Overstay

I have been trying to figure out how long a person has to wait until they are eligible to come back to the US after overstaying their Visa. I did find in another site that if they overstayed for less than 1 year the wait is 3 years, but if the overstay was 1 year or more, the wait is 10 years, is this correct?

Also if the person who overstayed their Tourist Visa had returned to their native country and has been there for 7 years and their children are now US Citizens, can one of the children apply for a permanent residency or even a new Visa for the parents? If so, can that be done right away or do they have to still wait the 10 years?

I appreciate the help and any advice on this situation.

Thank you.

They still have to serve the ban unless they qualify for a waiver which is very difficult to obtain; they can discuss waiver option with an attorney. The times you relates are correct. Only US citizen children age 21 and older whio meet income support requirements can petition for a parent.