Does submission of an FA application affect one’s chance of getting into a top school?

I think your question is, “Will my kid be rejected if my kid applies for financial aid?”

The answer to that is, “It depends.”

If your kid applies to places that are need-blind, then the potential financial aid need won’t matter at all. However, most places don’t have a lot of aid money to give out so you might not be able to send your kid there even if your kid is admitted.

If your kid applies to places that are need-aware, then if that place doesn’t like your kids as much as another kid who requires less aid, your kid might be rejected.

Make your budget. Run the Net Price Calculators at the college/university websites. Make a list with your kid of places that are likely to fit in your budget. See what the results are.

Your posts aren’t written in standard US English, with makes me suspect that you are an international or immigrant parent who isn’t particularly familiar with undergraduate education in the US. If I am correct about that, you may benefit from finding people from your own country/language group who are familiar with education here and who can advise you.