I am a Ghanaian by birth, a medical student in Romania who holds a Romanian EU residence permit. Can I travel to Serbia for 3 days without a visa?
According to the Serbian MFA
At its meeting of 30 October 2014, the Government of the Republic of Serbia adopted the Decision on visa free entry to the Republic of Serbia for holders of foreign passports having a valid Schengen, UK and other Member States' visa, or visa of the United States of America, and for holders of foreign passports having residence permit in the countries of the Schengen area, EU or the United States of America, which was published in the "Official Gazette of RS", No. 119 of 31 October 2014 and which will enter into force on 8 November 2014.
And from Timatic, the database used by airlines worldwide:
Visa required, except for Passengers with a residence permit, valid for the period of stay, issued by Romania for a maximum stay of 90 days
So yes, with your passport and Romanian residence permit, you can stay in Serbia visa-free for up to 90 days.
Don't forget, however, to request a "prijava karton" from the Hotel in Serbia, a registration form which you present to the border police (together with your passport and Romanian residence permit) when exiting Serbia