I am on a limited income and my kids refuses to help me financially, where can I look for subsidized apartments for an independent senior?

Every town has at least one apt. complex that is gov. subsidized. Sounds like you would qualify with your income (and you will need to "qualify" every year). Call your local office on aging and ask for a list of gov. subsidized senior apts.
The apartments in our town are really nice and charge one third of the regular rent.
good luck