The early guidance for this vaccine mandate appears to support medical and religious exemptions, for legal reasons. If you are in need of an exemption due to medical reasons, you should file for a reasonable accommodation (RA). You can find a link to the Accommodation Point (where you apply for an RA) and the medical documentation form needed here (see the information in the yellow box.)
For religious accommodation (RRA), email OEEOD@uspto.gov with the request. You will then receive further information.