As i carrying out simulations using the port instance in analogLib, I noticed that when i define a pulse and dc port, i have this offset of 310.mV on the output of the both the pulse and dc. Please let me know, as to what is the issue
First of all, it's a bit odd that you're using ports here, because they are driving a high impedance load (the inputs to the voltage controlled voltage sources). Since the ports have a 50 ohm impedance, the output level of the ports would only be the values you specify if driving a matched load. So in this case, I think you probably should have used a vsource instead.
However, the offset can't be anything to do with that (that would affect the amplitude). Since all the vcvs is doing is replicating the voltage across the output of the source twice, to give you a positive and negative incursion, the offset must be a consequence of whatever the vss node voltage is. Did you check that? Maybe it's not connected properly? The fact that the DC outputs have some oscillation (reasonably large oscillation) suggests to me that the vss node is not tied down and maybe floating?