EarlyStopping and ModelCheckpoint is what you need from Keras documentation.
You should set save_best_only=True in ModelCheckpoint. If any other adjustments needed, are trivial.
Just to help you more you can see a usage here on Kaggle.
Adding the code here in case the above Kaggle example link is not available:
model = getModel()
model.summary()
batch_size = 32
earlyStopping = EarlyStopping(monitor="val_loss", patience=10, verbose=0, mode="min")
mcp_save = ModelCheckpoint('.mdl_wts.hdf5', save_best_only=True, monitor="val_loss", mode="min")
reduce_lr_loss = ReduceLROnPlateau(monitor="val_loss", factor=0.1, patience=7, verbose=1, epsilon=1e-4, mode="min")
model.fit(Xtr_more, Ytr_more, batch_size=batch_size, epochs=50, verbose=0, callbacks=[earlyStopping, mcp_save, reduce_lr_loss], validation_split=0.25)