We consider a wireless communication system that consists of a transmitter, a receiver, and an adversary. The transmitter transmits signals with different modulation types, while the receiver classifies its received signals to modulation types using a deep learning-based classifier. In the meantime, the adversary makes over-the-air transmissions that are received as superimposed with the transmitter's signals to fool the classifier at the receiver into making errors. While this evasion attack has received growing interest recently, the channel effects from the adversary to the receiver have been ignored so far such that the previous attack mechanisms cannot be applied under realistic channel effects. In this paper, we present how to launch a realistic evasion attack by considering channels from the adversary to the receiver. Our results show that modulation classification is vulnerable to an adversarial attack over a wireless channel that is modeled as Rayleigh fading with path loss and shadowing. We present various adversarial attacks with respect to availability of information about channel, transmitter input, and classifier architecture. First, we present two types of adversarial attacks, namely a targeted attack (with minimum power) and non-targeted attack that aims to change the classification to a target label or to any other label other than the true label, respectively. Both are white-box attacks that are transmitter input-specific and use channel information. Then we introduce an algorithm to generate adversarial attacks using limited channel information where the adversary only knows the channel distribution. Finally, we present a black-box universal adversarial perturbation (UAP) attack where the adversary has limited knowledge about both channel and transmitter input.