LPR (EB3) for Naturalization

[FaithHopeLove]

Good day!

I have been a permanent resident for 6 years now.  I got my greencard through EB3 Consular Processing, which took 7 long years before it got approved.  When I arrived to the US, the job I was sponsored for was no longer available.  In short, I was not able to work for the company that I was supposed to work for.  I was given a letter from the company saying such.  Nonetheless, I have been employed through the years since coming to the US while filing taxes religiously and remaining to be a good resident with no trouble at all.  I have been a public employee for a number of years now and my job entails services to the community.

I want to apply for naturalization, as well as my derivative child (who is now a young adult and now gainfully employed as well).  However, I'm worried that this might create a big problem for us.  Somebody told me that it could be construed as fraud.   If my child applied for naturalization, would my information be reviewed as well?  Will they ask for my information during the interview?

Any thoughts on this?  Any advise what action to take?  Thank you, I'd appreciate your responses.