The title of this entry is mostly a misnomer. We’re not talking sources in regards to The Winter’s Tale, but source. Singular. There are a few elements that seem to have been influenced by other works, but they feel more like shouts-out or intertexts rather than stolen properties.
Near the start of Shakespeare’s career, in 1588, the novel Pandosto by Robert Greene was published. The prose romance concerned a King of Bohemia, the titular hero, who accuses his wife Bellaria of being unfaithful with his friend, the King of Sicilia. The rest of the novel’s plot is very close to the plot of our play as well: the self-deluded king orders that the baby daughter be killed or left for dead at sea. His wife and son both die. Time passes as the daughter is raised by a shepherd. She meets and falls in love with the prince of Sicilia.
There are, of course, deviations. Shakespeare swaps Bohemia with Sicilia. The names are different: Leontes/Pandosto, Hermione/Bellaria, Perdita/Fawnia, Polixenes/Dorastus. The most pronounced changes come at the end of the narrative. In the novel, when reunited with his daughter, Pandosto is overcome by guilt and commits suicide. Additionally, Shakespeare’s Camillo is a composite of two of Greene’s characters; Shakespeare also adds Autolycus, Paulina and Antigonus. Oh, and the Bear.
And that ending. Shakespeare goes lighter than Greene: there is reconciliation and resurrection rather in The Winter’s Tale, suicide in Pandosto.
Because of the timing of this play in Shakespeare’s career, it’s possible–though unlikely–that it wasn’t Pandosto that was the source, but its 1607 reprinting under the title Dorastus and Fawnia.
Those other “sources” are Boccaccio’s Decameron (which have may have influenced some speeches) and Plutarch’s Lives (some of the character names), but like I said those feel more like references to those earlier works and not borrowings.