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As per checking, it seems that the Square Payment Integration currently does not allow recurring payments or subscriptions. The available Payment Type for the Square Payment integration are sell products, collect donations or custom amount (user to will define the payment amount).
I will have to escalate the issue to our development team. We will inform you on this thread once the recurring payments has been implemented in Square Payment integration.
Unfortunately, this is not currently possible because square's api does not yet allow that type of usage outside of their own platform such as with our square integration.
However, if and when it does then we would gladly add it and update you to let you know.
So this means as of right now the only alternative would be to create recurring payments directly through their platform.