In this article, a new class of alpha skew truncated Cauchy distribution is proposed by considering Balakrishnan methodology and investigated some of its related distributions. This article also derive various properties of this distribution along with its moments. The proposed distribution is applied in modeling currency exchange rate data with some other existing distributions, viz., skewed Cauchy distribution, skewed truncated Cauchy distribution, truncated skew Cauchy uniform distribution, doubly truncated skew Cauchy distribution, and alpha skew truncated Cauchy distribution. Based on the model selection criteria, Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC), the proposed distribution has shown significant improvement in modeling exchange rate dataset.