The biological father of Kalysta Jordan-Potter was most likely a Muggle who at one point had a baby with Kalysta's mother. Her mother would later go on to abandon their infant daughter in an alleyway after witnessing her displays of underage magic. It is unknown whether the two had been married or even in a relationship at the time of Kalysta's desertion, or whether or not she had been a single mother. Ultimately neither of them were ever traced, and their daughter would later be adopted into the magical Jordan and Potter families.
Though it is chiefly believed that Kalysta is a Muggle-born, it was speculated at one point that her father might have been a wizard who had left her mother but still passed on his abilities, leaving her mother in the dark about magic and the existence of the wizarding world; however, there is no possible way of confirming this suspicion.