Current Transformer Secondary Current in 3 Phase 4-Wire

What you have missed is

1. the readings on L2 and L3 - do they appear true? They would tell us if the fault is total, or just one phase.
2. The full-scale reading for ammeter. There is a difference between an in-scale but wrong display and an over-range display. Some instruments, by design, display negative or over-range if an external wire is broken.
3. The maker of DSE6110 or the generator, without maker it is difficult to find specifications or manuals.
   

Yes readings on L1, and L2 appear true. The DSE6110 is a digital generator controller; therefore the ammeter is digital. Why the S1 of L3 is inputing high untrue current to the ammetter is what i seem to miss.

1. You have not given us a connection diagram, but usually the 3 phase CTs would have one common terminal, plus one for each CT.
2. Modern CTs, for use with high impedance electronic loads, may well have an internal load resistor and output a voltage to the electronics.
3. Consequently, 3 CTs would make 4 wires to DSE6110, with just 4 terminals on it for current. Older systems might have two terminals per CT, taking a current input.
4. A first step would be to find out how many CTs you have, and which is the common terminal, wired to all of them. Second would be to decide if you have the voltage or current system.
5. Does the genset have a separate or mechanical governor? A separate voltage regulator (AVR)? If they are you could (without worrying about effect on voltage or speed) swap over two of the CT inputs to the control, to see if the faulty phase moves from L1 or stays with it.
6. Have you looked at this DSE6110? Do the CT inputs go direct to the main controller? Or are there other integrated packages between, which could be faulty?
   

If the three phase load is balanced you might be having two CTs which is sufficient to show third current, so are you sure you checked the connections.

Yes, i checked connections are ok. What buffles me is why L3 would give high current reading.