There are unfortunately no trains from East Fishkill to Poughkeepsie. There is a line which runs through East Fishkill, but it is for the (infrequent) private use of Metro North and thus no public trains run on it. A good alternative option here is the Dutchess County Loop Bus, which apparently has a Hopewell Junction to Poughkeepsie route.
The trains don't run through East Fishkill to get to New York City, so a commuter's best bet would probably be to go to the Beacon Metro North Station and ride that down into the city.