Question: What was Telesphorus' father the god of in ancient Greek mythology?

Context paragraphs:
Telesphorus (mythology): In ancient Greek religion, Telesphorus (Greek: Τελεσφόρος "Telesphoros") was a son of Asclepius.  He frequently accompanied his sister, Hygieia.  He was a dwarf whose head was always covered with a cowl hood or cap.

Hedylogos: In Greek mythology, Hedylogos or Hedylogus (Ancient Greek: Ἡδυλογος ) was the god of sweet-talk and flattery and one of the winged love gods called the Erotes.  He is not mentioned in any existing literature, but he is depicted on ancient Greek vase paintings.  A surviving example on a red-figure pyxis from the late 5th century BC shows Hedylogos alongside his brother Pothos drawing the chariot of Aphrodite.

Theoi Project: The Theoi Project (also known as Theoi Greek Mythology) is a digital library website about Greek mythology and its representation in classical literature and ancient Greek art.  It serves as a free reference to the gods ("theoi"), spirits ("daimones"), mythological creatures ("theres") and heroes of ancient Greek mythology and religion.  Established in 2000, the website contains over 9,000 pages and 9,000 images.  The website also has a library of classical literature on the theme of Greek mythology, including the works of many of the lesser-known poets.

Melaina: In Greek mythology, Melaina (Ancient Greek: Μέλαινα  "Mélaina" , feminine Ancient Greek: μέλᾱς  "mélās" "black, dark"; Koine Greek: Μελανή  "Melanḗ" ) was a Corycian nymph, or member of the prophetic Thriae, of the springs of Delphi in Phocis, who was loved by Apollo and bore him Delphos.  Her father was one of the local river gods, either Kephisos or Pleistos of northern Boeotia.  Melaina was also identified with Thyia who is named as the mother of Delphos in other traditions.  In some legends, she is called the daughter of Persephone by Hades.

Asclepius: Asclepius ( ; Greek: Ἀσκληπιός , "Asklēpiós" ] ; Latin: "Aesculapius" ) was a hero and god of medicine in ancient Greek religion and mythology.  Asclepius represents the healing aspect of the medical arts; his daughters are Hygieia ("Hygiene", the goddess/personification of health, cleanliness, and sanitation), Iaso (the goddess of recuperation from illness), Aceso (the goddess of the healing process), Aglæa/Ægle (the goddess of beauty, splendor, glory, magnificence, and adornment), and Panacea (the goddess of universal remedy).  He was associated with the Roman/Etruscan god Vediovis and the Egyptian Imhotep.  He was one of Apollo's sons, sharing with Apollo the epithet "Paean" ("the Healer").  The rod of Asclepius, a snake-entwined staff, remains a symbol of medicine today.  Those physicians and attendants who served this god were known as the Therapeutae of Asclepius.

Batea (daughter of Teucer): In Greek mythology, the name Batea or Bateia ( ; Ancient Greek: Βάτεια) was the daughter or (less commonly) the aunt of King Teucer.  Her father was the ruler of a tribe known as the Teucrians (Teucri).  The Teucrians inhabited the area of northwest Asia Minor later called the Troad (Troas), and the term is sometimes used as another name for the Trojans .  Batea married King Dardanus, son of Zeus and Electra, whom Teucer named as his heir.  Batea gave her name to a hill in the Troad, mentioned in the Iliad, as well as to the town of Bateia.  By Dardanus, Batea was the mother of Ilus, Erichthonius, Zacynthus, and Idaea (future wife of Phineus).  Greek mythology also recounts Arisbe of Crete, a daughter of Teucer, as the wife of Dardanus, so Arisbe and Batea are usually assumed to be the same person.

Rhodos: In Greek mythology, Rhodos/ Rhodus (Ancient Greek: Ῥόδος ) or Rhode (Ancient Greek: Ῥόδη ), was the goddess and personification of the island of Rhodes and a wife of the sun god Helios.

Dionysus: Dionysus ( ; Greek: Διόνυσος "Dionysos") is the god of the grape harvest, winemaking and wine, of ritual madness, fertility, theatre and religious ecstasy in ancient Greek religion and myth.  Wine played an important role in Greek culture, and the cult of Dionysus was the main religious focus for its unrestrained consumption.  His worship became firmly established in the seventh century BC.  He may have been worshipped as early as c. 1500–1100 BC by Mycenean Greeks; traces of Dionysian-type cult have also been found in ancient Minoan Crete.  His origins are uncertain, and his cults took many forms; some are described by ancient sources as Thracian, others as Greek.  In some cults, he arrives from the east, as an Asiatic foreigner; in others, from Ethiopia in the South.  He is a god of epiphany, "the god that comes", and his "foreignness" as an arriving outsider-god may be inherent and essential to his cults.  He is a major, popular figure of Greek mythology and religion, becoming increasingly important over time, and included in some lists of the twelve Olympians, as the last of their number, and the only god born from a mortal mother.  His festivals were the driving force behind the development of Greek theatre.

Comus: In Greek mythology, Comus (Ancient Greek: Κῶμος ) is the god of festivity, revels and nocturnal dalliances, as depicted in the 1921 children's book, "Comus" by John Milton and Arthur Rackham.  He is a son and a cup-bearer of the god Bacchus.  Comus represents anarchy and chaos.  His mythology occurs in the later times of antiquity.  During his festivals in Ancient Greece, men and women exchanged clothes.  He was depicted as a young man on the point of unconsciousness from drink.  He had a wreath of flowers on his head and carried a torch that was in the process of being dropped.  Unlike the purely carnal Pan or purely intoxicated Dionysos, Comus was a god of excess.

Phelios: Phelios (フェリオス , Feriosu ) is a 1988 vertical scrolling shooter video game released for the Namco System 2 arcade platform in Japan by Namco.  A Mega Drive port was released in 1990.  The game features a plot loosely based on Greek mythology.  The player takes control of the knight Apollo, the god of the sun, who sets off on the legendary winged horse Pegasus, to rescue his lover, Artemis, the goddess of the moon, from the Titan, Typhon.  The game takes names and little else from Greek mythology in which Apollo, god of the sun, was actually Artemis's brother.  The game shows players an Artemis that acts as an stereotypical princess (but in Greek mythology, she was the goddess of the hunt, and took pride in never being with any man).

Supporting paragraphs: Telesphorus (mythology) Asclepius
Answer: medicine