The use of cryptocurrencies has led to an increase in illicit activities such as money laundering, with traditional rule-based approaches becoming less effective in detecting and preventing such activities. In this paper, we propose a novel approach to tackling this problem by applying graph attention networks with residual network-like architecture (GAT-ResNet) to detect illicit transactions related to anti-money laundering/combating the financing of terrorism (AML/CFT) in blockchains. We train various models on the Elliptic Bitcoin Transaction dataset, implementing logistic regression, Random Forest, XGBoost, GCN, GAT, and our proposed GAT-ResNet model. Our results demonstrate that the GAT-ResNet model has a potential to outperform the existing graph network models in terms of accuracy, reliability and scalability. Our research sheds light on the potential of graph related machine learning models to improve efforts to combat financial crime and lays the foundation for further research in this area.