I am graduating medicine in 2 years time. I am from Indonesia. I tried inquiring what the requirements are, but I have not been getting any straight answers thus far.
I cannot find anything about fellowship yet. But, about the residency training,
The Singapore government agency says
Enrolment into Training Programmes
... Graduands from overseas must secure an offer of employment as a doctor from MOHH or a local healthcare institution before they are eligible to apply. ...
For more details, please contact them directly.