The success achieved by conformers in Automatic Speech Recognition (ASR) leads us to their application in other domains, such as spoofing detection for automatic speaker verification (ASV), where the conformer self-attention mechanism might effectively model and detect the artifacts introduced in spoofed speech signals. Also, conformers can naturally handle the variable duration of speech utterances. However, as with transformers, the conformer performance may degrade when trained with limited data. To address this issue, we propose utilizing conformers in conjunction with self-supervised learning, specifically leveraging a pre-trained model called wav2vec 2.0, which is pre-trained using a substantial amount of bonafide data. Our experimental results demonstrate that our proposed method achieves one of the best results in the recent ASVspoof 2021 logical access (LA) and deep fake (DF) databases.