What to do this type of data

Since you have more than one target value for a specific value of the feature and because the Y values are have quite a large range I guess the nueral network finds it hard to converge. Try to normalize the target values so that it has zero mean and unit variance and then try to use any of the regression models like logistic regression, A CNN with a squared error to get a prediction. After that plot the ROC-AUC to determine the dominant regressor.