Here are a couple of options to bias the network towards the class you want:
1- Modify the class weights. For example, in order for your algorithm to treat every instance of class 0 as 5 instances of class 1, you can do:
class_weight = {0: 5., 1: 1.}
model.fit(X, y, class_weight=class_weight)
2- Modifying the classification threshold based on the ROC curve, as pointed out by Dave and AruniRC.
3- Oversampling the training samples from the class that you want to prioritize, e.g.:
X_neg = X[y == 0]
X_pos = X[y == 1]
ids = np.arange(len(X_neg))
choices = np.random.choice(ids, len(X_pos) * 5)
X_neg = X_neg[choices]
X_pos = X_pos
y_neg = np.zeros(len(X_neg), dtype=np.int8)
y_pos = np.ones(len(X_pos), dtype=np.int8)
X = np.vstack([X_neg, X_pos])
y = np.stack([y_neg, y_pos])
The problem you stated is generally a common problem in the case of imbalanced datasets, where you might have many more samples in one class compared to another (which commonly happens in medical datasets). Most of these points were taken from the Keras tutorial for handling imbalanced datasets.