wireing

My generator is a Troy-Bilt and only has the 120/240 four prong female plug for 30 Amp. There is no switch to select 110 or 220. The 110 outlets on that Troy generator are only 20 Amp so I need to use the 120/240 four prong outlet on that generator but only with 110 volt service to my RV.
I wired a four prong plug as follows: bare/ground wire to green screw/slot which is the prong that had the lock part on it. All the other screws were brass so there was no silver screw to attach the white wire to. I put the white wire at the bottom prong, directly across from the ground prong, which was marked “W” by that slot. The other two prongs are marked “X” and “Y”. I attached the black wire to the right side prong as you are facing the plug with the ground on top and the white wire on the bottom. I left the left prong open (no wires attached). I plugged in the cord and ran the generator. With a meter I put one lead on the ground wire and one lead on the black and got 110 volts. I left the lead on the ground and touched the white wire and got zero reading. I then touched the leads to the black and white wires and got a 110 volt reading. Is that correct??????????
Thanking you in advance.
Glenn