I am a resident of New York State but I received unemployment benefits from Pennsylvania.. Do I file those benefits on my PA taxes or NY Taxes? When I file NY tax, it says I owe tax now.

Unemployment benefits are not taxable in Pennsylvania. They don't even appear on your Pennsylvania tax return.

Since you are a New York resident, all of your income is subject to New York tax, no matter where the income is from. And unemployment benefits are taxable in New York.

There are many possible reasons that you might owe tax to New York, and it doesn't necessarily have anything to do with unemployment. The amount you owe is not tied to any particular type of income. It's based on your total income for the year and the total amount of tax that you had withheld. But if you did not have any New York tax withheld from your unemployment benefits, that certainly could have contributed to having a payment due.

I lived in NJ but worked in PA from jan to apr of 2020. Then I moved to NY. While I'm residing in NY, I collected unemployment from PA from may to dec. So, do I have to file PA tax return in this case? PA didn't withheld tax from my w2 or unemployment income.  Also, NJ and PA has reciprocal agreement. 

You do not need to file a PA return.  The income you earned while living in New Jersey was only taxable in New Jersey.  The unemployment income is not taxable in Pennsylvania at all but is taxable in New York.