Country
Jamaica
I have 2 sourced drinks connected to Jamaica. The label on each card says how: where it began, what the country is known for, what people drink there, or where the origin is disputed.
Drinks of Jamaica
Signature drinks and regional ones, with the evidence behind each. A drink marked non-alcoholic has no alcohol in the traditional serve.

Jamaican Sorrel with Rum
Christmas season
IconicRegional drink
A deep red, tart Christmas drink made by steeping sorrel, the roselle plant, with ginger, allspice and cloves, then sweetening it and serving it chilled. Rum is the traditional addition for the alcoholic version, especially Wray and Nephew White Overproof.
Sorrel is a Christmas tradition in Jamaica, and Wikipedia says drinks of this kind were introduced to the Americas by enslaved Africans. The Daily Meal names Wray and Nephew White Overproof Rum as the traditional rum. None of the pages opened give a Jamaican date for the custom.
Made with: sorrel (roselle) leaves, ginger, allspice, cloves, sugar, white overproof rum.
Confidence: lowEvidence: thedailymeal.com (opens in a new tab), en.wikipedia.org (opens in a new tab)

Planter's Punch
ContestedSignature drink
A rum punch of Jamaican rum, lime and sugar, listed by the IBA as an Official Cocktail. The IBA recipe pours the three ingredients into a small tumbler or a terracotta glass and dilutes with water, ice or juice to taste, with an orange zest garnish.
It is said to have originated in Jamaica, and the September 1878 issue of the London magazine Fun printed a rhyming recipe for it, in which lemon juice and sugar are rubbed together before rum and cold water are added. The pages opened give only the Jamaican attribution and the 1878 rhyme, and neither names an inventor.
Made with: Jamaican rum, lime juice, sugar cane juice, water or ice.
Confidence: mediumEvidence: iba-world.com (opens in a new tab), en.wikipedia.org (opens in a new tab)
Map data: Natural Earth, public domain.