Especially when applying to expensive schools. Will they reject me simply because I’m poor?
You posted this earlier:
How poor are you?
Poor enough to have an EFC of 0.
It’s complicated. My dad got a full ride scholarship to MIT (not ivy league but close) and came back to our 3rd world country to start his own company. He only makes 25k but that amount of money in my 3rd country is mathematically and literally the equivalence of an American making 400k/year. However, I’m still a poor kid in this country. That explains how my both my parents went to college and still poor af 
A school might be need blind, meaning that it purposefully won’t take your ability to pay into account in making admission decisions, so theoretically low income doesn’t hurt as far as being admitted (a separate issue of course from ability to pay if you get in, but a lot of need blind schools pledge to meet 100% of need). Another school might be need aware, meaning they might consider your financial situation in making admissions decisions, so theoretically it could be an advantage in getting in if you can afford to pay. Other schools don’t seem to pay attention to income one way or another and just admit you or don’t and it’s up to you to figure out how to pay if you get in. I don’t know where UVA falls in that regard. Regardless, you should be running Net Price Calculators with accurate numbers to get an idea of how much schools might expect you to be able to pay.
As far as what your previous thread seems to be asking, I have never personally heard of a school being “Ivy aware,” meaning that I don’t think any school will care that your dad went to an Ivy League school, whether or not he earns up to the potential that such an education suggests he could. Except that your dads particular alma mater might care to the extent that you are a legacy, which, if anything would work in your favor.
As noted above, it varies by college. There are many US colleges that will not admit an international students unless that international student provides evidence that they have the ability to pay.
UVa is need blind in admissions for US students. However, UVa and most other colleges typically do not provide financial aid for international undergrad students.
Assuming you are classified as an international student (and not a US citizen living overseas), and if you really want to study in the US, your best bet is probably to look for a college with an affordable sticker price of tuition. Another option is to attend college in a cheaper country, and transfer to a US college later, or endeavor to attend a US college for grad school. For some majors, grad students at some US colleges do not have to pay tuition, provided they serve as a research assistant or teach intro classes.
I’m a citizen so I’m probably good. Thank you bud.