The story
- Jamaican Creole · derived frombaby-father
- English todaybaby daddy
African-American Vernacular English (General American would be baby's daddy) 1990s, popularized in the 2000s; compare baby mama. Possibly from or influenced by same term in Jamaican English, from Jamaican Creole baby-father, alternatively due simply to grammatical similarities between AAVE and Jamaican Creole.
Etymology from Wiktionary, CC BY-SA 4.0.