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Walking is free…if that’s too slow but you’re still super cheap probably AirTrain JFK to subway to PATH in NYC to Newark Penn Station to a bus to EWR.
It’s not going to be super fast since you’re talking about changing between four different transit lines (Airtrain to subway to different subway to bus).
If you want to be even LESS cheap and faster, Airtrain to Long Island Railway to Penn Station in Midtown to an NJ Transit train to AirTrain EWR.
The trains involved aren’t making as many stops and travel faster.