Assuming you are from Nigeria, the Jamaican immigration website says that you will need a visa. https://www.pica.gov.jm/immigration/entry-visa-requirements
The best way to figure out whether you need a visa or not is to email the Jamaican embassy with a copy of all your travel documents (passport, expired green card and extension notice) and see what their response is. If they say, you do not need a visa, then print out that email and take it with you to the airport and show it to the airline if they try to deny you boarding.