New battery doesn't last longer than 1 hour! Also drains fast during "sleep"

Replace it with a genuine Apple battery, if you can find one. I could not find one with a cursory search.

Does anyone have any suggestions on how to fix this issue?

Perform an SMC reset. Read the instructions following the horizontal line below.

Supposed they are supposed to last even longer than the factory battery.

I have heard those claims too. They simply are not consistent with my experience. I no longer purchase nor can I recommend NewerTech, but if Apple no longer produces replacement batteries you may have no other choice. If that battery is still under warranty, see if you can return it for another one. One hour is clearly unacceptable.

For these few months I kept it mostly plugged in fully charged, which I know is bad for the battery.

Right, don't do that. Repeated attempts to "recalibrate" the battery won't help, so don't do that either.

The aftermarket SSD complicates matters. Complaints regarding Samsung SSDs are common. It's premature to conclude it is the sole cause or contributing to rapid battery drain, but removing it and replacing it with the original hard disk drive, if that is possible for you, would be an instructive troubleshooting step.

Power or other problems related to unexpected system sleep, shutdown, lights or fans call for anSMC reset. Read all the steps.

Before Resetting the SMC

Try each of the following steps in this order before you reset the SMC. Test the issue after completing each troubleshooting step to determine if the issue still occurs.

1. Press Command + Option + Escape to force quit any application that is not responding.
2. Put your Mac to sleep by choosing the Apple () menu from the upper-left menu bar and then choosing Sleep. Wake the computer after it has gone to sleep.
3. Restart your Mac by choosing the Apple () menu from the upper-left menu bar and then choosing Restart.
4. Shut down your Mac by choosing the Apple () menu from the upper-left menu bar and then choosing Shut Down.

Resetting the SMC on Mac portables with a battery you can remove

1. Shut down the computer.
2. Disconnect the MagSafe power adapter from the computer, if it's connected.
3. Remove the battery (to remove the battery - click here: MacBook or MacBook Pro).
4. Press and hold the power button for 5 seconds.
5. Release the power button.
6. Reconnect the battery and MagSafe power adapter.
7. Press the power button to turn on the computer.

Still having problems? Replace steps 6 and 7 with the following:

1. Reconnect just the MagSafe power adapter.
2. Press the power button to turn on the computer,
3. Then reconnect the battery.

Also, please post the same screenshot as above, but first unplug the power adapter. Wait a few minutes, then post the same Battery Information again. The information in your screenshot shows the power adapter connected and a fully charged battery, so your MacBook's power consumption isn't being measured.

At the time that screenshot was captured, that battery, fully charged, would be fully depleted in less than three hours. That's not acceptable either. If that is not consistent with the endurance NewerTech promised, I'd be inclined to return it.