Model transfer with limit to none label information

I have this problem I hope to get some help here. Say I have a type of product A whose measurements are X_A and an outcome property is y_A. y_A is a continuous variable. Then I can have a predictive model out of it using X_A, y_A.

Now I have a product B. It's similar to product A but not exactly the same, like an orange to a grapefruit. For product B, I have plenty of X_B measurements, but very limit to none y_B outcomes. Here X_A and X_B are from two different distributions, so are y_A and y_B.

I want to pick your brains on what methods I can use to transfer the model I obtained from product A and make it suitable to product B, meaning have ok-to-good performance in predicting y_B.

In experiment stage, there are plenty of y_B to verify the goodness of transferred model. But in reality the number of known y_B is few to none.

I am looking for suggestions other than supervised transfer deep learning, since the limited known y_B really will be few, like 10-20. And there won't be much variance in these observed X_B, y_B pairs.

Thank you in advance!