Input capacitor of an amplifier
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. OP's circuit.


  So now when the electrons from the ac signal comes, won’t the electrons present on the dc side plate repel them.


You are forgetting a couple of things:


For current to enter C1 on the left side then the same current must leave on the right side returning to the V1 source via R2 (or via R1 and V2). That's the nature of circuit theory. V1 is pushing charge around the circuit but it is a circuit.
Not that it matters terribly, but the right side of C1 has positive charge on it so according to your theory negative charge should be attracted to the left side of C1.
V1 has voltage or "electro-motive force". It can push charge around a circuit.


Notice here that I am deliberately using the word charge as current is not always electron flow. This also allows you to think in terms of conventional current flow and will save you much confusion.

So what is happening then? What has helped me in understanding circuit theory is to thing of capacitors as having a voltage across them (which could be zero) and in the short term the capacitor keeps the voltage across it constant. In Figure 1 C1 is charged to V2/2. Now as V1 voltage increases the left side of C1 is "lifted" and the right side lifts by the same amount but immediately starts to discharge through the combination of R1 and R2 back to the V2/2 voltage. You should be able to follow this through and see what happens when V1 decreases and goes negative.