Happy to help with this one. To start, Square works with any US-issued and most internationally-issued cards bearing a Visa, MasterCard, American Express, Discover, JCB, or UnionPay logo.
Having said that, it sounds like you might be referring to a specific HSA/FSA card. Licensed health care providers can process these types of cards just like any other cards. If you selected the Medical Practitioner, Medical Services, or Dentistry business category when you signed up, you shouldn't have any issue accepting these cards. If you believe your business category needs to be updated, get in touch here.
This article has more info about accepting HSA cards: https://squareup.com/help/us/en/article/5085-accepted-cards.
Sean
he/him/his
Product Manager | Square, Inc.
