Inverting amplifier saturation with capacitor
When a parallel C(is labelled as C2) is added, the output is
  saturated. What is the explanation of this?


At 2 kHz, the 5 nF cap has an impedance of  about 16 kohm. Because it is in parallel with a resistor of value 300 kohm, the op-amp gain is increased about twenty times and it is much more likely that the op-amp output will saturate.


  How can i tackle this C which negatively affect the output?


Put a 15 nF capacitor across R5 to "balance" the effect of the 5 nF across R1. However, the op-amp output may show signs of instability so, also try a 100 ohm resistor in series with V1.