Hi I have a Connecticut Electric 30 amp transfer switch box that has a male 4 prong L14-30 which i have the cable for. However, on the generator side I have a 3 prong, and a 4 prong (shown in image). I dont run any 240 in my house. I dont run anything over 30amp and all breakers are either 15 or 20 The question is what are my options to connect it?
Your L14-30 cord is totally incompatible with both of these sockets. In other words there is no advantage to going with the one on the left merely because it is twist-lock.
You need the one on the right. You will need to buy or build an adapter cable to it.
I dont run any 240 in my house. I dont run anything over 30amp and all breakers are either 15 or 20
You mean to say "I don't have any 240V appliances and no 240V circuits that I know of". That might be so, or might not. *Multi-Wire Branch Circuits are 240V circuits which resemble two independent 120V circuits, but require 240V power to avoid overloading the neutral. Your house's supply is most likely and nonetheless 240V, as is your transfer switch.
- If you supply only 120V to this, only half your circuits will work. - If you "cleverly" split the 120V, then you'll overload the neutral on any MWBCs.
Since your generator is capable of delivering 240V, you might as well do it. Path of least resistance.