You have a place there called Mamoun's that is open until midnight at least, if you like middle eastern coffee. And there are some other restaurants/bodegas with seating that are open really late or even 24/7 and serve coffee, but they aren't all great for studying and the coffee may not be that good.

There's an excellent boba shop / cafe with coffee right across from the main Starbucks, that stays open until 10 or 11pm most days i think. There's also at least one other boba tea/coffee place by the Green that's not as fancy, but is open until 10pm most days I think. Pistachio also stays open late some nights.

There are TONS of really nice cafes for studying in New Haven, but generally they are open until 8pm or 9pm. I guess it's tough to find baristas who want to work at a coffee shop after 9pm these days. No 24/7, sit-down, studying type coffee shops that I'm aware of. Gather East might be open later some days.

At least it's not like Hartford where everything closes at 3PM (or is closed altogether thanks to COVID!)